It's not impossible, it's just very difficult, impacts every single part of the stack, and is very difficult to justify.
Also, a specific potential use of FPGAs is for pattern matching on large amounts of text/data: If you do it at all, you're likely to do it often; and it can't be a custom implementation since the circuit depends on the specific pattern.
It is typically simply cheaper to deploy FPGAs in released products when the volume is small, while it may be cheaper to use full custom when the volume is in the millions to hundreds of millions, in the cases where either solution is functionally workable.
That includes amortizing the non-recurring engineering costs over the total units, which is typically higher for full custom than FPGA -- although sometimes they are actually in the same ballpark.
Aside from that you are correct; people sometimes imagine that most any application can be significantly accelerated with FPGAs, but even in the cases where fine-grained parallelism is present to be accelerated (well-known not to be the case for all application areas), the FPGA solution space is decreased by the solution space where full custom makes engineering and financial sense.
There are FPGA-SoCs out there that are mostly FPGA, and that seems like the way to go if you want to combine FPGAs and CPUs, otherwise they should probably be on separate power and heat budgets.
What we have is still a CPU and a GPU. Separate. Discrete. The inclusion changed nothing about what kind of software we can write or problems we can solve. Back when APUs were still just a slide in a powerpoint deck, there was a lot of talk about how this could "change everything" because of the radically different type of compute you could do on a GPU.
The closest thing to this is the coin mining craze, but everyone is gravitating towards the fastest hardware for that. And that's not your APU.
Although I dont see that happening soon. Mostly because no one has the interest in doing so. What most likely will happen is that Apple are so far ahead in this game they started to take notice and work on something.
On Server it is very different though. Tiles and Chiplet will finally means FPGA can have their own node and optimisation while sitting next to CPU without all the complexity of trying to get them into the same silicon. Although the cost of specific software optimisation for specific task will likely means they only goes to HyperScaler.