For that price, I'd say no, If it was cheaper then maybe, I couldn't justify that much for an old CPU when a 11700k is cheaper, newer and has a better upgrade path. Boards might be a little more but the cost you just saved from not getting the old 9900kf can go towards the board.
9900k/kf is an ok option for a GPU up to about an RTX 2080/2080S/3060/6600XT/6700XT class GPU at 1080p anything above that you would start to see some bottlenecking - comparatively vs. better CPU. 1440p gaming would be less affected by stronger GPU's with a 9900kf.
A 9900kf is still a good CPU if you already have one but at this stage a poor investment if you are looking to buy one. As it is the top CPU un its range it tends to hold its value. I am still running a 9900k and it is still fine (1440p 4070 super) but I wouldn't buy one at this stage.
For a similar price you could likely get a b550 and a 5700x on the AM4 platform new which would outperform the 9900k.
Yup, if you are going to do Intel, 12th gen is where the deals are right now. If you are on a strict budget, you can also find some decent deals back on AM4 AMD platform. The nice aspect of AM4 is that AMD is STILL releasing stuff for it. The bad aspect of AM4 is that it can be a BIOS (compatibility) nightmare in regard to what CPU/mobo will actually come up working on install. If you go that route, make sure to pick a motherboard that offers the BIOS flash feature build into the board.
If you are near a Microcenter they have a nice combo going on the 12600kf.
on am4 you could easily pair it for a bit more money with a x3d chip which would eek out a bit more performance with the faster cache https://pcpartpicker.com/list/CP4LmD
Flash the mobo for the 14th gen CPU. Mine came with a late BIOS but you never know. It's might be too old for a new CPU.
You don't need a CPU or RAM to flash. Use a USB stick and Q-flash. As long as the motherboard is connected to a power supply, it will update.
I normally avoid F models. If you can afford it, buy the 14100 non-F. You never know when the GPU will crap out, or when BIOS will act up and require integrated graphics.
Upgrade to a 14500 later on if you need more cores/performance. It's $240 right now but if you can find it cheap, grab it. Or if you can stretch your budget to $400.
Don't run unlocked K CPUs on that motherboard. And forget i7 or i9. But if you examine the i3 you might see it's enough for more than just esports.
I have an i3 12100 on that motherboard and it flies in Win 11 even without a GPU. Struggles a little bit in Satellite Reign 1440p but Northgard and RimWorld run great. With a 1070 or 4060, it would be a lot of power for very little money.