When I make my designs with the STM32H747X, I'll see if I find it interesting to make 6-layer PCBs and use vias in pad to facilitate routing. I have to route a lot of tracks from that chip to connect an external parallel SDRAM among other things, and I guess it will be tricky.
Well, theoretically you should be able to fanout any 240pin BGA in 3 routing layers (when 1 of them is the mounting layer), it would probably be unwise to try and do it on a 4-layer board. 6-layer is a reasonable minimum, especially if you want proper power and ground planes (which will greatly enhance the performance of your SDRAM interface). Depending on the density, an 8 layer board could be reasonable too.
Depending on your future plans with the design, I might not want to use the "free" via in pad from JLPCB. It might lock you in to this vendor, and you might want to have options to shop with the design for later production runs.
If its a one-off, I would totally go for it!