DEAR MISS MANNERS: I would like your opinion on the proper etiquette for when a car stops to allow a pedestrian to cross the street. I believe the polite thing to do is to give the motorist some signal of gratitude and walk quickly across the street. Some feel no need to rush.
GENTLE READER: In the ancient world -- by which Miss Manners means the days before Same-Day Shipping -- there was an understanding that most accounts did not need to be settled on a daily basis.
Dinner guests issued reciprocal invitations at a later date rather than paying for dinner with a present, food or even cash. Friends repaid favors as opportunities arose.
In the case you mention, your haste is understandable, since you are unlikely to encounter this motorist again. But this does not modify the rules. Acknowledge the kindness with a gesture, as you suggest. While there is no necessity to speed up your crossing, there is also no prohibition. There is, however, a prohibition against reciprocating with a rudeness -- stopping mid-street, for example, to check your emails.