OP, you are asking a VERY BIASED crowd and getting answers that show that bias. It's like asking those strongly political (party) one way or the other which is the better party/platform? Or a group of passionate Coca Cola drinkers, what is the best soda? Of course you are going to get pounded with Apple HP recommendations because we are very much Apple people... and HP is the only speaker Apple makes.
IMO, sound quality is as important as video quality. So if you've put some money into a great TV and a great streaming box, don't shortchange the audio. If nothing else, the speakers you choose will outlast... and be just as good... long after both the TV and AppleTV have been outdated/failed and replaced... probably SEVERAL times. Good speakers can easily last 10-20 or more years. There are people in this forum with speakers purchased back in the 1970s-80s that still sound as good as day 1.
Since HP "smarts" depend on audioOS (a fork of tvOS), I expect HPs to be software obsolete much sooner than the speaker portions themselves go bad. Note how second generation cannot even stereo pair with first generation from only a few years ago. That complete "smarts" dependency for use dooms the speaker portion to be "thrown out with the bathwater" when those "smarts" age only a few years... just like we have to replace iDevices and Macs over and over even if the tech guts are still fine.
And without HP "smarts" they are useless. In addition, with no AUX input, they are heavily "married" to Apple sources & hardware. What if you want to put up an antenna and get free over-the-air HD? What about a game console? What if you want to hook up cable? Blu Ray player? What if Aunt Meg brings a VCR over to show the old family movies? How do you get all that non-Apple stuff playing on HPs?
HP is also limited to stereo at best. There are ZERO Apple rumors about going beyond stereo. A great home theater setup has been beyond stereo since about 199X. One can definitely hear a difference between stereo and- say- 5.1 surround sound because there are actual speakers behind, a center channel speaker for clearer voices and a sub for superior bass vs. what HPs can provide. Our ears can easily hear that difference. See post #8. That person is RIGHT!
Now, before the ADF jumps on this post to defend HPs, I fully admit HPs are great. They sound great. But their best use is as originally intended: music in rooms where you want great-sounding music but are not wired for sound. HPs sound surprisingly good for such a compact package. This use can work too, but it's basically a big improvement on the stereo speakers that came with the TV... not a home theater surround sound audio base.
So, if budget is going to stay so lean, I agree with post #6: Sonos Beam Soundbar as a start with an eye towards building out a full 5.1 (or more) system over time. If budget is not so pinched, I suggest the top-rated Sonos Arc as a starter with the same goal over time. If you catch the right refurb offer, it is not that much more than two HPs and it sounds incredible, is much more open and is made for your target use.
And if you can use what you might spend on an iPhone or Mac or two that will wear out or be made software obsolete in only 3-7 years, I suggest doing some thorough research to find yourself a great 5.1 or 7.1 surround sound setup: receiver + 5 or 7 speakers + subwoofer and going quality all the way (so you can be enjoying these to their fullest even 10-20 years from now). If budget is not constrained at all, maybe add a few more speakers above for full (& true) ATMOS (not the faux ATMOS implied by soundbar or 1-2 speaker marketing).
Whether the Sonos soundbar or this receiver option, you can start with as little as a single speaker or two and then build out the rest of the system over time. Either approach is much more OPEN than HPs, so you can easily hook any other source of video or audio up to it and enjoy it on your best speakers too. Both Sonos and good Receivers have full Airplay 2, so most of the benefits of HPs are available (the "smarts" shift to your AppleTV, iDevice or Mac, which you'll be regularly updating anyway). Apple Music is available on Sonos and you can play it from AppleTV, iDevice or Mac to a receiver-based system. I do this all the time myself.
Apple people love Apple stuff, so this will assuredly get pushback from Apple fans. Again, I agree HPs sound great. I just don't see them as ideal for this purpose even if they sort of work. You titled this thread "BEST option for TV speakers" and I wouldn't crown HPs as that... only best if limiting one's considerations exclusively to speakers from Apple Inc.
If you want to maximize the audio of your home theater, do it like the pros: there is no cinema or IMAX theater that only has 1 or 2 HPs down front somewhere. Go watch a movie and before the lights go down, take a good look around. You'll see many speakers down front, above, behind, left & right, etc. Why? Because that yields true theater sound... not 2 little cylinders or spheres parked down front. Replicate a version of THAT kind of setup in your home and your ears will be delighted by ANY source of sound for probably 2+ decades from this ONE purchase.