I've spent my hifi life trying to get the most for the least money. That's usually meant buying very good used or demo gear, then upgrading a piece at a time when I have the opportunity.
I lived with a NAD (Masters Series) M32 integrated amp with built-in DAC and phono stage and an M50.2 digital player/server for many years and enjoyed them a great deal, but I eventually wanted to improve all (six) areas they encompassed. That required pretty much starting from scratch.
Since replacing my amp with a Modwright KWH 225i, I've added a separate Modwright phono stage and bought an Okto dac8 DAC, which I later replaced with a Denafrips Terminator DAC. I also replaced the M50.2 with a Pachanko Labs Constellation Mini SE. Again, the Modwright, Denafrips and Pachanko gear was used or demo, and I sold all of the previous components.
I guess my recommendation would be that if you tend to hold on to your gear for a long time, a well-regarded integrated device could be an excellent solution with added price efficiency and strong synergy between functions (my friend has an integrated Lumin streamer/DAC in his $200k system). But if you like to upgrade a bit at a time, you might want to look at separates.