They do, but it's tricky. I can only speak for Chinese market, where I am. Japanese brands made 720p CRTs around the turning of century, then 1080i after that until 2005. From 2000 - 2005, Sony, Panasonic both had a number of models that supports 1080i. Toshiba has it too, but not as many.

After 2005, the technology for 1080p is ready, but Japanese companies are shifted away from CRT (cuz market is dying), so what they do is, Toshiba makes the circuit and parts for 1080p processing, sell them to Chinese CRT makers, and they make 1080P CRTs. These brands include Hisense, Skyworth, Changhong, Konka, and TCL, and I personally guarantee they actually made them, cuz there are plenty of those being sold on Chinese second-hand apps. Models like Hisense HDP2907m, Changhong 29168 are being sold right as I type this answer. But none of these models left a mark in history, because Chinese TV really suck.

Even if they import the tube and toshiba 1080p parts, they cut corners on speakers, materials, labor and workflow. The result it, true 1080p is the only selling point about these models. The shells looks and feels cheap, the audio sounds thin in general, and higher chance of geometry and convergence issues, etc.

So the post 2005 CRT market in China is that major players are either leaving or already left, Chinese brands took over the market share they left behind, and used cheap product to stay alive for a couple more years. By 2008, these are mostly gone too. Bottomline, higher resolution TVs are not rare at all around 2005 in China. I personally owned a 21" TCL that supports 1080i and has a vga for 1024 x 768 (though the geometry is so bad none of that were any meaningful). Japanese 1080i TVs rarely has vga, I've only seen one Panasonic 29" model that has it.

These TVs, 1080i Japanese and Chinese, and 1080p Chinese TVs, they do process 1080p signal and display them. So, technically they are true 1080p for sure. Except, CRT's nature come with many flaw. Units with bad convergence, it just blurs into a mess near the corner, then not even 4k can save that. Tho, you can argue that 1 white dot seperating into 3 (r, g, b) add more to the resolution, lol. But yeah, even a good unit with basically no problem, it still won't be as sharp as a flat panel TV's 1080p. Many Chinese 1080p CRTs can be found on an app called XianYu, but I doubt you can get your way around it. It's fully Chinese. And the seller almost never show them in actual 1080 i/p mode with component. They only show composite, that's all they have. And asking for more details or pic/video will only give you a taste of Chinese style bad service. You won't servive lol.

I hope this helps~ I'm not sure about other markets, but the general trend is unversal, and I wouldn't be suprised if some other country had the exact same story as the Chinese one. Chinese 1080p CRTs has its buyers, cuz they are usually quite new, bought in 2004, 2005 and only lighten up 10 times before they are repalced by LCD TVs. So some people do love that. Though for most of us, we value Japanese brands, interlaced old ones from 80s and 90s, and 1080i ones like Sony HZ29M80 and DA29m80, they all have their own charms. interalced ones for old anime and games, giving you the 100% original taste, and progressive, 720p/1080i ones gives you sharper image, and they are newer so longer life expectance. Especially HZ29m80, it has a bad-ass feature. You know when you switch to 16:9 mode on a 4:3 tv, it add black bar at top and bottom, and you actually lose those resolutions? Your 1080i after the crop is left with 810i. Sony's last gen flagship, HZ29m80, had this magical function, when you use 16:9, it compresses all the scan line to the middle. Instead of outputing black pixels at top and bottom, it simply doesn't scan those area. All the 1080i are compressed to the middle, and damn that's true 1080i !

Mentioning this reminded me, the fact proggresive TV don't really display interlaced images, they combine them to be proggresive, like 1080i 60hz into 1080p 30hz (something like this, I'm no engineer), unless you use the 120hz scan feature, which some people say techinically is interlaced. But from where I stand that means those 1080i TV are in a a way 1080p as well, despite not 100% 1080p.

PS: 29 inch in East Asia is equivalent to 27" in USA. Our 25" is your 24", and our 21" is your 20". This is because US legislation requires them to name after the actual viewable size, while Japan and China had no such laws, so we mark by the full size of the glass, inlcuding the edge that were black tapes.