Usually it turns out that if the place is shady enough for a microinverter solution to produce significantly more than a string inverter, then it still produces absolutely so little (due to all that shading) that investing in the more expensive system never pays for itself. I would primarily avoid installing PV in mediocre or poor places, because there is no lack of good places (if you look at the big picture).
But of course, there can be other type of motivation than just money. If you want to maximize the amount you are producing, then you are limited by the install locations you have, and maximizing production with microinverters could be emotionally the right thing to do.
String inverter does not care about the "weirdness" of the shading pattern. But if the minimum MPPT voltage is say equivalent of 6 panels (quite usual rating) and you have 10 panels out of which 5 are seriously shaded (so only 5 produce), then it falls below the minimum voltage and goes close to zero while microinverters would still produce 50%. But if this happens "all the time" then the question indeed is how much you are paying to be able to produce 50% of rated power. Like, you pay 30% premium to produce only 50% of an "optimal" system. Given long payback times of any PV install it makes no sense.
On the other hand, continuing with the same example, if you shade 3 panels out of 10 then string inverter and microinverter produce roughly the same: string inverter produces a tad below 70% of total rated; microinverter is able to get some power out of those shaded panels (but not much because, doh, they are shaded) so maybe it produces 75-80% of total rated during that condition, but loses that extra power, if not more, in generally 1-2%-point lower efficiency and usually higher idle power draw, which affect the system all the time.
TLDR:
* Partial shading of 20-30% of the roof for hour or two per day or so: just get a string inverter and verify you exceed minimum voltage most of the time
* Significantly more shading than that: don't install PV at all
* If you are desperate to get some power out of such crappy location, then microinverters or optimizers.