But they generally don't have a patent that covers anything real. Even ignoring the situations where the patent is indefensible through defects in process or due to prior art, the claims in these patents often don't actually read against the businesses being sued.
The problem is that it takes tens of thousands of dollars per patent to get an opinion from your own lawyers about whether the patents bear on your products or processes and you pretty much have to do that even if you never go to court.
If someone has (what you have called) 'a legitimate patent' then they have the right (whether they use the patent or not) to then pursue legal action to either stop use of the patent or to settle for money damages.
What companies don't like is someone coming along with the ability to engage legal help that they wouldn't be able to do with out the attorneys that are handling this (to gain a payoff for themselves which well attorneys do for other things).
However while this seems different than similar things that happen (with actual companies with legal resources) it's really just the same thing just by different parties.
If let's say General Electric has a patent on something and you use that patent GE can come after you (and probably will). Same as with large companies defending their IP (trademarks).
"GE defending a patent they use in their products" and "an LLC with one patent as an asset and no real business outside of defending said patent" are two entirely different situations, even if legally they're the "same."