Personally, I don't think this seems like a good idea. The game is balanced around the availability of these treasures.
The Kingdom piles change from game to game, so the only reliable element for your deck is treasure at 3 and 6 coins respectively.
The first player to buy a Gold already has a statistical advantage in Dominion, but this would enhance that advantage even further, since late-peaking players might not be able to GET any Gold.
It seems to me that, depending on how MUCH you limit, this change would have one of two effects:
No effect, because there's still more Silver and Gold than your players buy anyway. In many of the games my group plays 5 Gold per player would seldom run out, for example.
An overly punishing effect. You got 6 coins this turn, but there are no decent 5-cost Kingdom cards and the Gold is gone! You just got screwed.
You say "This would create a little more competition in getting treasures into your deck" but when I play Dominion I'm always competing to get treasures into my deck. If an opponent lands 2 or 3 Gold before I get one, I know I'm in trouble and had better pull off something amazing if I'm going to have a chance. Making the piles run out won't make me any more competitive, it'll just harm everybody later. I'm already always keeping other players' treasure levels in mind, because that determines how soon the Provinces may run out and whether I can even count on being able to afford Provinces or should just go for Duchies.
If the intent of this change is merely to discourage players from playing Big Money, I don't think this is the way to do it. Big Money is not an optimal strategy and will lose frequently to even relatively simple Action-based strategies once players figure them out. Play the base set a few times buying one Smithy or Laboratory+Chapel and see how long they keep playing Big Money!
It also feels like this change would bog down the middle-to-end game of every game as you would be unable to keep the treasure and victory levels of your decks balanced. Even if everybody got exactly the same amount of Gold during the build-up, your decks will all get slower and slower as you start buying the Provinces, since you won't be able to offset those with more Gold.
All in all, the game was definitely designed so that Treasure is not expected to run out - the Intrigue rules even say "these cards are intended to be in abundant enough supply to not run out". I think there are good reasons why Silver and Gold are effectively unlimited, and I don't think limiting those piles would make for much more fun in the long run. Experienced players will already be competing for Gold regardless of the supply, and will already be tracking their opponents' treasure levels to adjust their strategy.