What are the typical limitations for capacitors integrated into silicon chip?
On chip capacitors take a lot of chip area making them expensive. I'm currently working on a process where they can make metal capacitors of 2 femto Farad per square micrometer. So a 100 pF capacitor would have take up an area of 50000 sq um so 500 x 100 um.

But these capacitors can handle only up to 10 Volts or so, nowhere near your 350-400 V requirement.

Maybe there are specialist high-voltage processes in which high voltage capacitors can be made but I doubt that. Edit: Doubt taken away, there are, see comments.

For 350-400 V you need a strong and/or large dielectric which can withstand the fieldstrength. This is not easy to fit in a small size (like an IC).