Web devs support multiple browsers for the same reason desktop and mobile software developers code against multiple operating systems: some of their customers prefer those systems, and when you ask a customer to switch their framework to support your product you risk they'll say "no."
The reason web developers care about those customers varies from dev to dev. Some believe there is value in a heterogeneous ecosystem of browser implementations. Some have a few high-value customers who refuse to switch (or, in the case of e.g. Microsoft, cannot switch because enterprise constraints are restricting what browser stack they're allowed to run).
But the point stands that when you support multiple browsers, you don't approach ideal user experience (in terms of performance and reliability) for all your customers by throwing your fingers in your ears and proclaiming "That browser is out of spec!" when you find a quirk---you do what you have to do to make your code run on, around, or in spite of the quirk.
