WASHINGTON — President Obama wants to cut down to size those too-big-to-fail banks. But his vow on Thursday to rewrite the rules of Wall Street left many questions unanswered, including the big one: Would this really prevent another financial crisis?

The president’s proposals to place new limits on the size and activities of big banks rattled the stock market, but banking executives were perplexed as to how his plan would work. Indeed, many insisted the proposals, if adopted, would do little to change their businesses.

Moreover, it was unclear if the twin proposals — to ban banks with federally insured deposits from casting risky bets in the markets, and to resist further consolidation in the financial industry — would have done much if anything to forestall the crisis that pushed the economic system to the brink of collapse in 2008.

Mr. Obama appeared to be leaving crucial details to be hashed out by Congress, where partisan tussling has already threatened another reform the president supports — the creation of a consumer protection agency that would have oversight over credit cards, mortgages and other lending products.