An overly long reply
A sincere question: If the three branches of government "should be so constituted that the members of each should have as little agency as possible in the appointment of the members of the others," then why does the executive branch nominate members of the judicial branch? The framers of the constitution had so much confidence in the wisdom of the elitist Senate that the Senate would seem to be a a more natural choice of nominator (with the House confirming and the president having a veto). Doesn't that seem more consistent with the rest of the structure of the government?
Having 100 people of at least two parties coming to consensus upon a nominee seems less prone to corruption than one potential tyrant choosing his own overseer.
I simply don't know how or why they decided the president should nominate justices. Do you?
First of all, I probably should have quoted the relevant paragraph from Federalist 51 in full.
In order to lay a due foundation for that separate and distinct exercise of the different powers of government, which to a certain extent is admitted on all hands to be essential to the preservation of liberty, it is evident that each department should have a will of its own; and consequently should be so constituted that the members of each should have as little agency as possible in the appointment of the members of the others. Were this principle rigorously adhered to, it would require that all the appointments for the supreme executive, legislative, and judiciary magistracies should be drawn from the same fountain of authority, the people, through channels having no communication whatever with one another. Perhaps such a plan of constructing the several departments would be less difficult in practice than it may in contemplation appear. Some difficulties, however, and some additional expense would attend the execution of it. Some deviations, therefore, from the principle must be admitted. In the constitution of the judiciary department in particular, it might be inexpedient to insist rigorously on the principle: first, because peculiar qualifications being essential in the members, the primary consideration ought to be to select that mode of choice which best secures these qualifications; secondly, because the permanent tenure by which the appointments are held in that department, must soon destroy all sense of dependence on the authority conferring them.
Ok, as to the specific question: why should the President nominate judges and not the Senate? The first part of the answer is in Federalist 78:
The manner of constituting it seems to embrace these several objects: 1st. The mode of appointing the judges. 2d. The tenure by which they are to hold their places. 3d. The partition of the judiciary authority between different courts, and their relations to each other.
First. As to the mode of appointing the judges; this is the same with that of appointing the officers of the Union in general, and has been so fully discussed in the two last numbers, that nothing can be said here which would not be useless repetition.
In other words, the Framers saw the appointment of judges as not significantly different from the appointment of all other officers of government, like, say, the Secretary of State. So what did they have to say about the appointment of those officers of government? From Federalist 76 (Hamilton):
It will be agreed on all hands, that the power of appointment, in ordinary cases, ought to be modified in one of three ways. It ought either to be vested in a single man, or in a SELECT assembly of a moderate number; or in a single man, with the concurrence of such an assembly. The exercise of it by the people at large will be readily admitted to be impracticable; as waiving every other consideration, it would leave them little time to do anything else. When, therefore, mention is made in the subsequent reasonings of an assembly or body of men, what is said must be understood to relate to a select body or assembly, of the description already given. The people collectively, from their number and from their dispersed situation, cannot be regulated in their movements by that systematic spirit of cabal and intrigue, which will be urged as the chief objections to reposing the power in question in a body of men.
…
The sole and undivided responsibility of one man will naturally beget a livelier sense of duty and a more exact regard to reputation. He will, on this account, feel himself under stronger obligations, and more interested to investigate with care the qualities requisite to the stations to be filled, and to prefer with impartiality the persons who may have the fairest pretensions to them. He will have FEWER personal attachments to gratify, than a body of men who may each be supposed to have an equal number; and will be so much the less liable to be misled by the sentiments of friendship and of affection. A single well-directed man, by a single understanding, cannot be distracted and warped by that diversity of views, feelings, and interests, which frequently distract and warp the resolutions of a collective body. There is nothing so apt to agitate the passions of mankind as personal considerations whether they relate to ourselves or to others, who are to be the objects of our choice or preference. Hence, in every exercise of the power of appointing to offices, by an assembly of men, we must expect to see a full display of all the private and party likings and dislikes, partialities and antipathies, attachments and animosities, which are felt by those who compose the assembly. The choice which may at any time happen to be made under such circumstances, will of course be the result either of a victory gained by one party over the other, or of a compromise between the parties. In either case, the intrinsic merit of the candidate will be too often out of sight. In the first, the qualifications best adapted to uniting the suffrages of the party, will be more considered than those which fit the person for the station. In the last, the coalition will commonly turn upon some interested equivalent: "Give us the man we wish for this office, and you shall have the one you wish for that.'' This will be the usual condition of the bargain. And it will rarely happen that the advancement of the public service will be the primary object either of party victories or of party negotiations.
In other words, when SG says:
Having 100 people of at least two parties coming to consensus upon a nominee seems less prone to corruption than one potential tyrant choosing his own overseer.
Hamilton would disagree pretty strongly, and it’s hard to argue with him that in practice appointments in the Senate would not quickly devolve into horse-trading.
Federalist 76 is also interesting in that it includes this nugget of relevance:
To what purpose then require the co-operation of the Senate? I answer, that the necessity of their concurrence would have a powerful, though, in general, a silent operation. It would be an excellent check upon a spirit of favoritism in the President, and would tend greatly to prevent the appointment of unfit characters from State prejudice, from family connection, from personal attachment, or from a view to popularity. In addition to this, it would be an efficacious source of stability in the administration.
I mean, sort of, if the nomination is high-profile enough (e.g., Harriet Miers). But clearly not in less visible cases (e.g., Michael “Heckuva Job” Brown).