They do (or did?). My home NAS is running a Sandy Bridge Intel Celeron with ECC memory. Support seems to be randomly distributed thought through the product line[1] though and obviously depends on the motherboard manufacturer to implement it as well.
In general, Intel has a problem with branding. Their product lines are confusing mess requiring looking up each specific part to get a list of features it does or does not support. There's little rhyme or reason to it.
I got bitten by that back in the Core 2 era. When I built my very last Intel system, around an Intel DG43NB board, I picked up a Q8200, thinking it would be a great bang-for-the-buck chip. Little did I realize from the store display that the Q8200 was the only Core 2 Quad that lacked virtualization support.
The DG43NB died prematurely, due to capacitor plague. I didn't shed any tears for it.
Of course you need to know what you're looking at, the suffix of the number matters a lot (eg 7100 vs 7100U), but that is nothing Intel-specific. A Ryzen 2700 and a Ryzen 2700U are very different processors as well.
Its not because they are "very different processors".
If you look at the products that are actually compatible with your system, it's not confusing at all. Pentium/Celeron/i3/Xeon = has ECC, i5/i7 = no ECC.
For me, the reason to go ECC was just to prevent silent file corruption. With 64 GB, the math is in favor of me seeing bit flips. Moreover, I tend to put my machine to sleep, rather than shut it off, which also increases the likelihood of memory errors. I wouldn't say I have a highly specialized workload outside of the occasional VM, consisting of large files, for development. A lot of it is I just didn't want to deal with silent corruption of family photos & videos, even if the underlying file formats are pretty resilient.
Personally, I think the situation should be flipped. Everyone should run with ECC these days and only run without for specialized environments like gaming where you want to squeeze out every FPS you can. Faster memory isn't going to matter for most situations.
But for everything else, it's a scale of needs, sure the low-end would be a gaming console or graphics memory, but if that gap gets smaller, uptake and usage will scale as that advantage becomes cost effective at various consumer levels.
But having the option of choice, is and always been a huge plus for any consumer - AMD makes that choice far more accessible than Intel. Though I do see a mobile phone maker going ECC as the turning point in uptake and making that price gap more palatable in the end.
If you use it just for media consumption and playing games, anything goes.
A good power supply and ECC RAM make a very stable PC.
Whether one cares about that is one's own tradeoff.
A few i3 CPUs support ECC, though.
All desktop segment chips with ECC have i3 designation.
See:
https://ark.intel.com/content/www/us/en/ark/search/featurefi...
I hope that in a few years time that ECC will become standard, as for many it is driving a car without a seatbelt.
This and with security exploits (rowhammer), ECC would be the solution that is a price gap that for many, is still one that can and should be closed.
That all said, it would only take the one or two big mobile manufacturers to go ECC and marketing virtu the whole security and integrity aspect for the rest of the market to follow suit. Which would be a bigger driver in reducing the price gap premium over non-ecc memory. Which is how I see things panning out as mobile phone makers are running out of sell features to add and this would be an easy one for the premium market of phones out there today. Also one in which would go down very well for that feature alone.