So, is using a cpu without an integrated graphics card not a "wise"
choice in any case?
The quick answer is: No, you do not need integrated CPU Graphics (If I understand the double negative in the question).
Longer answer: As long as you have sufficient cooling for your system, you should not see a real difference in CPU operations, except in the difference you can expect from different CPUs generally.
However the choice is, as always, a factor of the money you want to spend vs the power of the machine you want to build vs the versatility of the final machine.
If you want to spend a bit more to experiment with integrated Graphics then go ahead. Otherwise, if you are already committed to using a dedicated GPU, I would say you did not need the integrated graphics with the CPU. Indeed, you will get much higher graphics performance from a dedicated graphics card or even Motherboard-integrated-graphics.
To be clear: The only limit to a CPU without integrated graphics (compared to a CPU WITH integrated graphics) is that it cannot render graphics.
What I'm "worried" about is this: is a cpu with an integrated graphics card capable of doing some operations that other cpus can't? (Of course I'm talking about when the dedicated gpu is running fine)