You do need to take care with using your own seed compost to start seeds off. It will not be sterlilised (unless you do so), and the bacteria etc in the soil will increase the risk of damping off or the seedlings being otherwise affected.
How would you sterilise it? We have a hot bin, would compost from this be sterile and at what temperature?
This provides some guidance:
https://www.law.cornell.edu/cfr/text/40/appendix-B_to_part_503No. 1 is specific to compost, and recommends 55
oC or higher within-vessel for 3 days (that would be your hot bin).
No. 3 is for sludge, not compost, and recommends 180
oC or higher for 30 minutes. Hotter, for a shorter period of time. It would probably work fine for compost.
The recommendations are part of laws that are meant to treat human disease-causing pathogens. PROBABLY would also work on plant pathogens(?) Not intended for plant pathogens though.
If I was doing anything in the family oven, I would gain concurrence from your OH (advice I would give to anyone!). Maybe get an inexpensive metal pot with metal lid just for compost (possibly at a car boot sale?).