The Supreme Court is about to hear a case which asks if there are limits as to whom a sitting president can hire & fire. Although seemingly a minor judgment, there are obvious large questions about Executive limits and general checks and balances.
Are you referring to the case Lucia v SEC? If so the case is not about the limits to whom a sitting president can hire/fire. The case is about the Administrative Law Judges within the SEC and whether or not they are considered "officers" of the United States and should be considered as such under the appointments clause of the constitution (The appointments clause of the constitution requires officers to be appointment by the president, department heads or the courts).
The Administrative Law Judges "Administrative law judges serve as independent adjudicators. Under the Administrative Procedure Act and the Commission's Rules of Practice, administrative law judges conduct public hearings in a manner similar to federal bench trials, at locations throughout the United States. They preside at and regulate the course of these hearings, which may include setting filing deadlines, issuing subpoenas, holding prehearing conferences, and ruling on motions. Following the hearing, the parties may submit briefs, as well as proposed findings of fact and conclusions of law. The administrative law judge prepares an initial decision setting forth his or her factual findings and legal conclusions and, where appropriate, determining whether sanctions are warranted. " https://www.sec.gov/page/aljsectionlanding
The question before the court is that whether these ALJs are officers of the U.S. and if so they should be appointed by the president or appropriate department head. IT ISN'T a minor judgement at all. In fact it has implications, as you said, for our system of checks and balances. This case can decide the direct control of a portion of the federal bureaucracy and make it harder for Congress to shelter the bureaucracy from partisan influence. But to address your question I couldn't find presidential appointment numbers online past 1996. If you want to find out how many people the President has to appointment the Plum Book is very helpful. The Plum Book is issued to every incoming administration and lists all of the positions that the President has to appoint. In 1996 Bill Clinton had to appoint over 8,000 people, in the 2016 Plum Book it was over 9,000. I took a look at the 1980 Plum Book but they didn't list any numbers from what I saw but it is about 160 pages long. I'm sure for Reagan we're looking at similar numbers as well though in 1980 and I'm sorry but I didn't check for 1880 (Im at work) but I'm sure the amount was still pretty high.