I suspect a lot of the flakiness is not the chip itself but the fact that, because it's cheap, the bottom-of-the-barrel manufacturers will always use it instead of the significantly more expensive alternatives, and then further cut corners with the board layout and design.
Ironically, the only problems I've had with NICs were on an Intel and a Broadcom.
> I suspect a lot of the flakiness is not the chip itself
Most certainly. Doesn't change the fact that Realtek being present is a huge redflag, even if it's not a cheap device, regardless of whether it's realtek's fault or the OEM/ODM/SI that integrated them into the system in question. It basically screams "we phoned this part in", though it's certainly not always true, it's true enough that I refuse to use them (be it by disabling them or just opting for entirely different hardware so I can avoid that headache).
Broadcomm is certrainly better than Realtek, but it's still a "Replace at soonest possible convenience" tier as well. Intel is far far more reliable in my experience (save for some of their combo bluetooth/wifi cards, but their dedicated wired ethernet cards have always been great for me. The i210/211 class of integrated bottom tier ones can be hit and miss though.
Ironically, the only problems I've had with NICs were on an Intel and a Broadcom.