1. How do you distinguish legitimate and illegitimate patents. I guess you have to agree on some arbiter, like courts of law. So that's how we are in the current situation
2. Notwithstanding the issue around deciding between them, most larger patent holders have a huge portfolio of "clearly" legitimate and illegitimate patents, and they are using both (you don't need to sue to use the patent, just threats are enough)
3. If you ever spoken to a patent lawyer, the whole process is about making the patent as broad as possible without disclosing how to actually do it (at least if you are using the technology yourself). So one might argue it's about making the patent as illegitimate as possible, because then the patents are actually useful (otherwise they are just to easily worked around) .
Of course there's no easy way to distinguish _all_ patent (applications) this way but that one would not be accepted.
The issues you raise are certainly valid and reasonable but notwithstanding not the point of contention here. The trolling part is the one that comes from what is perceived as illegitimate claims/ patents.
There are, in fact, four alternatives here and not two:
1. Producing company, legitimate patents; 2. Producing company, illegitimate patents; 3. Non-producing company, legitimate patents; 4. Non-producing company, illegitimate patents.
What I think grinds most people's gears are #4 suing #1 (or #3, though I don't think _this_ is common.)
So your attempt at making this out to be a (false) choice between #1+2 on the one hand and #3+4 on the other is disingenuous.