For sure...
"I don't want to see political ads from a local election across the country."
They should be targeting eligible voters. If a local election is taking place across the country, then, of course, you shouldn't be seeing the ads.
"There's also no reason for me to see an ad for the Republican primaries if I am voting in the Democratic primaries. Etc"
No, this defeats the purpose. We should be trying to expose people to more viewpoints - not creating more echo-chambers.
Now we can expand on those rules to dictate who can see what, but no matter who views the ad, it would likely be bland, and confer no new viewpoint at all. Lest it fall afoul of FEC rules.
What we're really talking about with FEC rules, is a return to the middle, because extremist views can be shut down by pointing out misleading content in the ads and subsequently rejecting them. Whereas the bland, meaningless stuff will always be free of any misleading content, and be subsequently approved.
I'm not sure what media you consume, but TV and radio ads always seem filled with misleading content about political rivals.
> Surely there are some parameters that would make sense? I don't want to see political ads from a local election across the country. There's also no reason for me to see an ad for the Republican primaries if I am voting in the Democratic primaries. Etc
I think the answer is somewhere in the middle. A couple factors need to be balanced: the ads need to have the minimum targeting to not be wasteful and pointless, but they can't be so narrowly targeted that oversight by the media and voting public becomes difficult.
I think the right balance is something along the lines of: 1) coarse-grained geo-targeting allowed down to an MSA at the narrowest and 2) no targeting based on interests, demographics, or ideology.
There are some parameters that make sense, for example targetting congressional districts.
What I'm mostly against is zip code, ideology/interest, racial/sexual/etc factors being taken into consideration.