I think the latest PHP APIs are the least of your problems if you're running sites with code that hasn't been touched in 15 years:
* new security threats that have been discovered in that time which needed to be coded against (In the last 15 years, a lot has changed with the approach we have to building secure sites).
* newer web standards and browsers - thus compatibility on the client side might now be an issue.
* different computing paradigms (we use touch interfaces where hover-over menus wouldn't function. There's a massive range of different client side screen resolutions and aspect ratios these days too).
* different methods of sharing content (for some types of sites, supporting OpenGraph and Twitter Cards is pretty important if you depend on your content getting exposure from "word of mouth").
* different user expectations (a 15 year old site is unlikely to look any good compared their modern counterparts. While that might not matter for some sites, if you're trying to generate traffic from the average layman, then they might be put off and prefer a site which is more aesthetically pleasing).
So if someone is trying to port 15 year old PHP code to a new server, then I'd expect they'd want / need to do a sizeable amount of rewriting anyway - regardless of API compatibility. In this instance, API compatibility is the least of their worries as you can at least just use the 'find/replace' tool in your text editor to fix renamed APIs, where as fixing the other issues (eg switching from the older method of dropping variables into an SQL string, to the current preferred method of parametrized SQL which negates the risk of SQL injection attacks) will take much longer.