Each vote is equal and ensures local representation.
The only difficult part would be moving away from one local rep equals one vote. In many cases it will be a percent so one rep could have 1.4 time that of a vote and some may have only .67 of a vote.
So it's not as simple as it seems, and that's beside the awkwardness of totalling up fractional votes for each parliamentary debate. You'd need fully electronic voting for that, which may well be a good idea anyway, but it's a big step.
There are already existing methods that get very close to fully proportional representation while keeping local representation, and don't require fractional votes, so we should just use those. For example https://en.wikipedia.org/wiki/Mixed-member_proportional_repr...
E.g. to take Norway as an example because I know it well: Norway is split into 19 electoral regions (for a population of ~5m), but could easily have been split into even smaller regions with the use of a few more levelling seats.
People cast a vote for a party list (which they may amend, to affect ordering of the candidates if they wish, but most people don't), and seats are allocated to the party with the most votes first, and then counted votes are removed, and the threshold for the next seat is adjusted using the Webster/Sainte-Laguë method.
This initially gives a pretty good proportional result. Any "wasted" votes after the allocation of the regional seats gets summed up at a national level to be used to assigned levelling seats - one seat in each constituency is currently assigned as a levelling seat assigned based on the national vote, so that parties due a levelling seat should ideally get it in the constituency where they came closest to winning a direct seat where there is still a free levelling seat when "their" seat is being allocated.
The end result is that while constituencies are larger, most people will generally find that there's a representative in their constituency that is at least sympathetic to their issues, whereas under non-proportional systems the geographic link is largely a sham for partisan issues - my local MP (in the UK) used to be a Conservative, that I could safely bet on would oppose anything I cared about and nothing I might want to bring up would get a positive response. I'd rather have actual representation than a geographic link to someone who opposed the policies of about half of his constituency (and the problem remains now - I have an MP now that I like, but about half have one that will oppose their issues).
[1] https://en.wikipedia.org/wiki/Webster/Sainte-Lagu%C3%AB_meth...
Ignoring the fact that your statement isn't true (as pointed out by others). The current system does not ensure local representation either. People generally vote for their favorite party, and do not base their decision on the policies of particular candidates. On the off chance that you actually hear anything out of your local representative, it will most likely be about notional level issues rather than anything happening in your district. When non-partisan issues come up, your rep is more likely to side with whichever company gave them money, and it'll be decided behind closed doors, it'll be added as a rider deep inside some bill you won't read. On the off chance that you actually read that part of that particular bill, you'll never know who was responsible for it.