I've got way too many thoughts on this and it's very nuanced, more a podcast discussion IMO (hint hint at any creators out there), so the lists are not exhaustive nor are the caveats/discussion paragraphs.
1. Prize pool needs to do a few things:
a. Reward performance
b. justify a time investment
c. market the tournament (actually a big factor)
d. give prestige/credibility to the tournament
2. Beyond that you have other things like:
a. allow players to go full-time or part-time (linked to point b above)
b. provide incentives for players to want to progress
c. market the game as a whole
d. push/market sponsors (x amount sponsored by y company)
e. attract higher profile players
f. provide intensity (win this match and get x amount more)
Distribution is also largely dependant on absolute prize pool and number of players, if there's "only" $500 I'd suggest the winner get a bigger %, if there's $50,000 I'd suggest the spread is more even spread.
Different tournaments will prioritise these goals differently, for example if I want the top players to compete but only have a small budget I might give the bulk of the money to the top 4/2, I might even restrict the tournament to a small number of player (example show matches).
If I want a more serious series where matches before the grand and semi finals are interesting and intense then I would give a more even spread but with distinct jumps for progressing through the stages.
So in true AOE2 tradition my answer is "it depends", there's no one right way to distribute funds. A variety is probably best so long as the distribution is properly thought out and goals are clearly established beforehand.