How about a little more, like 5 tuners, 6, 7, 8, and so on?
agree with above posters.
Not enough (perceieved) market value to justify the cost.
Most people are assumed to watch live TV, and record a show or two at the same time, max.
When we did an an STB design for the national cable company here in 2014, I upped the specs from a two-tuner (one for recording, one for live tv) to an 8-tuner design (4 for FCC live tv, 4 for recording or "hopper" use).
The cost of the tuner was not that much more, it was a move from discrete tuners to Full-Bandwidth Capture (FBC) w. 8 digitial "taps" (tuners). The key driver for this was the user experience - our brief was to create the best viewing experience possible within the limitation of cable-tv. This meant using 4 tuners for live TV browsing, and 4 for recording.
While the design team was repeatedly challenged on the cost of the FBC tuner w. 8 taps, we prevailed. And had great reviews in the press when we launched.
Channel change time was almost instantaneous. Recording 3 programs at the same time covered 99.9% of needs of our customers. The box was (for these but also other reasons) perceived to be the by far "fastest" on the market.
At least for just for a few months, it was really greaty to be basking in the "fastest box in the country"-light. It sure was good to see that the intent of making the (almost) fastest experience possible came to bear fruit.
But the thing is - when you look at the cost of the box, then then 8 "tuners" added a few dollars more in HW cost.
Which is crucial to scale. Especially if 80% of your audience are happy with two "simple" tuners.
What more, though, is that the features enabled required more complex UI, and more complex software on the box, which in turn meant higher development, support and maintenance costs etc.
We were going for the "best-in-class User Experience". Not all companies have that luxury. Some only go for the "best price/value ratio".
So, for most ("average") tv companies relying on delivering live (or time-shifted live) tv, 8 tuners are expensive on many fronts, and scaling this to a few million customers is probably not worth it.
For enthusiasts, you can build a PC with multiple tuners cards, and have 12 tuners in a tv-headend (or equivalent) setting, but it will be a minority interest group.
So I think the answer to you question chimes in with the other posters - it's not worth it in the bigger picture (both HW cost and SW development and maintenance cost).