It doesn't but it accumulates cruft and since then new libraries emerge which you might be able to reuse instead of writing your own thing. Just as an example: Boost first appeared in 1999 so very likely at least early on no one used it.
Of course you could do that, but the existence of a bit of code that's survived that long within a project that's been around for 20 years doesn't mean nothing new has happened. Mozilla invented a whole language to make it easier to write browser in; I don't think they won't have considered using Boost or whatever much less radical approach we might come up with here won't have been considered and invested in.
The last time a major browser originated, RAM was measured in MB, CPU freq in MHz, and the iPod was the thing that the one trend hunter your friend knew was about to buy.
The major browser platform today, smartphones, did not exist. PDAs did not even have wireless internet yet.
The basis for the functionality of the browser is due for a reimagining.
Chrome forked from Webkit, which forked from KHTML, which apparently dates from 4th November 1998, so Chrome's base is 25 years and 7 months old tomorrow.