On the contrary, as you indicate yourself, elections are won or lost at the national level, so people apparently already don't give a shit about local issues in national elections (which makes sense).

You have just pulled a compelete 180 from your previous comment of:

It really depends on what the people think is more important: calling attention to a particular national issue, or getting their very local issues represented. FPTP forces them to always choose the latter option.

My point still stands though. My local MP lost a different election because he was really bad at looking after our region. No of our local issues got dealt with so he didn't get elected again. FPTP is really a hard system to get elected on. It requires the MP to be good locally and be a member of a party that is viewed positively. If either are not true they don't get elected. With PR the only requirement of the MP is that their party is liked nationally. It doesn't matter if a few thousand people dislike MP Joe Bloggs so long as those people like Party Purple that he is part of as the ballet paper would say Party Green Party Purple or Party Yellow. Sure it's not black and white and some shit MPs would cost you vote even with PR but not to the same extent as they can in FPTP as the shit MP isn't tied to a particular region unless you arbitrarily place MPs in regions. In which case if a region was very pro party yellow but nationally party purple was the favourite you'd assign your shit party purple MPs to the region as no matter what they won't vote for you anyway and the voters in that region could do nothing about it as the yellow vote is too weak nationally to get seats.

Parties that are elected with a low turnout are weak too.

Not really, they have the same amount of power no matter what the voter turn out is of x seats out of 650 you just have a less content public, doesn't really change the power though unless the people revolt which takes a major major issue.