To clarify, it won't be all the same random events. The seed determines some things like the contents of the traveling cart, mine levels, night events and geodes. Other things, such as whether a given day will be rainy, also use other variables, such as how many steps you have walked.
So if two players use the same seed, they will have a broadly similar but not identical experience. It would make a competitive run more fair, but only if they weren't told the seed ahead of time - otherwise they could look up the set events or even do a play-through ahead of the competition.
Because they determine the traveling cart, some seeds lend themselves to early community centre completion. Back on the old forum we did a search for seeds that might give a chance of completing the community centre very early in Y1. 102148953 worked very well in 1.4... I completed the CC on Summer 17 with that one!