There’s no question that a quality integrated is a better value, particularly at the ~$10K price point. I have an integrated in a 2nd system and it’s an easy solution with good sound. But I have to say, an integrated as a main system is a commitment, and if you lose flexibility to swap out the pre section more easily down the road for instance. It’s all about knowing yourself and your priorities.
As you get beyond the $10K level the performance of separates starts creating some "separation" from integrateds in my view. Having an amp and preamp share a common power supply or even the same box (and power cord) starts creating a loss of fidelity compared to what separates can deliver. EMI/noise has to be dealt with in the box, isolation is difficult etc. Add quality interconnects and most of the better separates will sound better than the better integrateds.
To me it boils down to your price point, being ok/not ok with having limited flexibility, and having physical space. If you want the best possible solution for a $10K budget and you don’t mind the inflexibility you’re not going to do better than a quality integrated. As you move higher price there is no question that you will get better fidelity with separates - it’s all about priorities.