Just the opposite. It's priced entirely by monthly page count; IIRC the first 100 pages per month are included in the base fee ($3 a month, last I checked), and you pay an extra $1 for every 10 pages in a given month. Since it's a subscription, they just tack on the extra charges after the fact. (I think the extra page rate, at least, depends on plan; trust their pricing info over mine, ofc.)
In exchange for the subscription, your printer automatically requests replacement ink cartridge sets to be shipped whenever the installed set runs low. That doesn't cost extra, and if there's a rate threshold past which it stops happening, I've never hit it.
Ultimately, this works out, by design, as a terrible deal for printing documents, sold entirely on the idea of convenience. But if you're printing photos, in which every sheet that goes into the printer comes out with ink all over it, the deal turns upside down, because the incremental cost of that ink is zero. And, as a nice side benefit, you get fresh cartridges shipped to your door a little before you need them, without having to think about reordering at all.
Last I checked, MSRP for a full CMYK set of first-party cartridges for an Officejet 8610 is $160. At $3 a month for the "Instant Ink" thing, it takes a little over four years to add up to the same cost as one regular replacement set.
The only true drawback I can see here, for the photo printing use case, is that while a printer is enrolled in Instant Ink, it won't take cartridges not provided through that program. That might be a headache if you want to keep an extra backup set handy, but it's never been a problem for me since I set my printer up with the program some time in 2017. It definitely does prevent using remanufactured, refilled, or third-party carts - but, again, that's never been something I felt the need to do while getting first-party ones for ~free, and I doubt I'll change my mind on that as long as HP keeps playing themselves this way.
(For what it's worth, I thought twice about describing all this in such detail, just in case somebody at HP might notice and care enough to make a change. But what the hell, right? This stuff would take five minutes of BI work to find out, given the data they must certainly have for the program to operate as it does at all. That they leave it as it is tells me they don't care, and why would they? Almost all the program's enrollees are no doubt getting the bad end of the deal, and I'm sure it helps them sell printers, so it's no skin off their nose either way.)