Can Konsole automatically save a log of all sessions on closure?

I’ve added script -a to my profile(s) as a stopgap

but I don’t want to have to save every session manually to get a readable (not to mention .HTML, so colour preservant) log for each session invoked by konsole.

Consequently, can I force Konsole to automatically save a file (somewhat like spectacle can) per session whenever I close a tab or konsole itself?