Yes, but the other factor is, with much cheaper platinum available, new applications are likely to be found which were previously ignored due to cost. Today, for instance, (this is an unrealistically simplistic example) if you could make something out of either copper or platinum, with copper not working quite as well but still fairly close, you're obviously going to choose copper because platinum is so expensive. If platinum is now cheaper than copper, you're going to choose that instead.

However, this does make me wonder: are there any applications where platinum would actually make more sense than what we're already using? It doesn't conduct electricity better than copper, for instance. So aside from catalytic converters and jewelry (which we already use platinum for, so it'll just drop the cost rather than expand the market), what is it good for?

Secondly, what about other metals? Surely these asteroids have other valuable metals besides platinum, such as iron and nickel. Considering how much we use copper, we could really use a copper-rich asteroid.

Platinum, along with other metals like iridium, are valuable for industrial purposes. Their price would fall if supply increased, but it wouldn't collapse. Demand would also increase as the price falls and it would probably still be valuable when it levels out.

would this be a problem? not sure. will certainly require adjustment in how we do things but in the long run it would benificial

But not to zero. It's not going to be worth trillions, but it might still be worth enough to bring a tidy profit.