I have a site which has key location landing pages in the footer which have been there for a long time. I know that these are not best practice and we should remove them. However, this could have a negative impact on the link equity to these pages. Is it worth removing them for best practice?
Links in the page footer are not bad practice per se.
The article you mentioned in your comments refers to a very specific type of common footer link which, being something that could be building links to one site on a large scale, could fall foul of Google's policy on link schemes.
It sounds like what you're doing is a good faith effort to serve user experience, i.e. put direct links to key locations in the page footer. That's a fairly conventional practice common on, for example, hotel and car rental websites. As long as it's done within reason, there should be no cause for concern.
There's arguably a wider issue in that, if you're finding a need to use the footer to link extensively to main content, it might indicate your main navigation needs attention.
You should be fine. Where I've seen this be a problem is where a site simply has a ton of keywords and links that server no other purpose but to push a higher ranking. Search engines are smarter about identifying that, these days and pushing those out of or lower in the rankings.