this is all kinda debatable.
My honest philosophy is, if you want to play your old console on an HDTV, go with only the expensive stuff that gamers are recommending. If you want to save money, go with emulation.
There are issues with emulation. Saturn, Dreamcast, PS1, PS2, Xbox, N64 emulation is inconsistent or nonexistent, and even better emulated consoles such as SNES have incompatibilities, inaccuracies, and hacks to make it work.
There's no reason to go with a cheap offbrand converter on amazon or ebay that we all try to warn people about. Those crappy devices are always going to be less authentic than emulation... which is free. They truly have no place in a gaming setup.
"Less authentic than emulation" when one is using real hardware and one is not is nonsensical. Moreover, for players who don't care about input lag, they may find that a budget transcoder or even scaler is actually sufficient for their needs. Especially if they don't care for scanlines and are apathetic about having perfect scaling.
Either you go full authentic with your hardware by investing the money the right way, or you go full emulation. The only acceptable middle ground between those two extremes is simply connecting your console straight up to your HDTV and hoping for the best. It will be at least as good as any off-brand device.
there are many acceptable middle grounds. Budget transcoders/scalers, internal mods to both a console or a tv, buying a cheap secondary tv, etc. etc.
There's simply no reason to waste money on untested stuff not built for gaming. There are no "hidden jewels" of hardware out there when it comes to scaling/converting video signals. Trust me on that.
Most of these devices have been tested. Their faults are largely understood if you're willing to do some research. Indeed, most of these cheap devices are one of a small handful of devices, rebranded. Their issues are, generally, that they don't actually take RGB (in the case of SCART -> HDMI boxes), however with some of these this can be modified trivially. Moreover, as Sheepy said and as others have sought out, there is a dirth of good research as to TV compatibility with offspec systems, as shown by the various quirks discovered in the development and feedback with the OSSC.
Like, I get what you're talking about and I largely agree, but your terms are too strong for basically no reason. People here won't be recommending a poor quality 50$ scaler, because it does have many issues, but if someone just simply can't afford a framemeister or OSSC or similar, and wants to play, say, a PS2 title on their HDTV, telling them "just emulate" when that is nearly as obtuse and presents entirely different problems, is ignorant, reductionist, and ultimately bad advice.