There are in fact parts that have CPUs included. However these aren't always the best route. Sometimes you don't want a CPU in the design at all, since software is SLOW compared to RTL designs for certain applications (DSP, Data acquisition, etc).

Xilinx has a number of SOC parts that bundle ARM cores alongside FPGA fabric, and they're very tightly coupled to make passing data between them very efficient. These include the Zynq and Versal families.

There are already some open source cores out there, including NEORV32. There are also closed source ones, like Xilinx's Microblaze IP. Which comes in both ARM32/64 variants, as well as RISC-V now.

The FPGA itself is just the chip. You can find them pre-installed in development boards though, but these are more expensive. But at least they might of a microprocessor if that's what you want.

And if you're fed up with Xilinx, check out Lattice semiconductors. They have a somewhat more open ecosystem