Or is time better spent analyzing particular games (like a match between two masters)?
In general, is it better to play more, and analyze a few of those games, or to play less, and analyze most of them, or even play a less, and still only analyze a very few selected games? What is the most professional attitude towards learning?
Should aspiring chess players analyze all of their games?
It all depends on the result of the game.
Every single game that you lost was because you made at least one mistake. If you don't correct your mistakes you will continue to lose to the same kind of mistakes. The only way you are going to stop making the same mistakes, same kind of mistakes is by analyzing your games, identifying what you are doing wrong and correcting it.
Analyzing the games you lost is the one constant of the life of a player who wants to improve.
Analyzing the games you won is nice for your ego but in general does little to make you a better player.
Analyzing the games you drew can be very useful for identifying the "one that got away". If you were winning, or thought you were winning, and the game ended in a draw then it is useful to find out where you went wrong. Either your judgement was wrong and it was always more or less even or you really were winning and you made a mistake that let him get away. This is often a problem in endgames.
Every single chess game is considered to have "mistakes", because chess is still within the select group of unsolved games. Now if we redefine the word "mistake" taking into account the level/quality of play (measured by rating, for example), we find out that we always make mistakes, even when we win. Take this situation: you play against a much higher rated opponent. There is little chance that you will win the game. Your opponent sees more and he wins. Did you make a "mistake"? With the practical meaning of mistake, I don't think so; you probably didn't have a chance. But according to a theoretical meaning, comparing the game to that (still unknown) perfect game of chess, there surely will be mistakes. Even from your highly rated opponent.
My point is that you may not have made a mistake, but you will anyway benefit from analyzing your games, including the moves of your opponent. Moreover, I think that you must analyze all of your games, regardless of the result (I would, however, skip some fast blitz games). The closest best game that we can find is that analyzed by a well-known engine. And luckily nowadays it could be effortless: lichess.org and other sites allow you to analyze a full game, presenting you with alternative better moves:
One last advice: also analyze your opening! You don't need an engine to do that, but an Opening Book. These are opening moves considered best for both sides, catalogued according to statistics, looking at thousands of games over the years. There are many free opening books out there.
