1) Caliborn wants to be "Bros" with Dirk-> Doc Scratch is Lord English's own customized Puppet Dirk, designed to delegate all the hard work of timeline maintenance Caliborn doesn't want to think about to a smartass supercomputer Halquis subservient to his will.

2) Lord English is Caliborn's fantasy of exerting Power, the single and only thing he values (and the single and only thing he admires about Jake). In a sense, Lord English/Doc Scratch is a twisted, dark fantasy mirror of Jake/Dirk as parsed through Caliborn's vision.

3) Caliborn also sort of wants to (and this is gross, bear with me) couple with Calliope in some sort of fucked up Cherubfreudian way-> Doc Scratch acts as roleplay rendering of Calliope, with the little suit and a white magnum weapon and liking to talk a lot all echoes of her

3a) (I didn't come up with this take/insight, I was linked to it in a forum post somewhere that I can't dig up now but it was really good back then I wish I could remember the source.)

4) Anyway, Conclusion:

Doc Scratch is Lord English's little boywife puppet rp

Final addendum: Jake also likes delegating all the hard thinking/logistic work of any situation or risk management to Dirk so he, like Lord English/Caliborn, can just focus on the fun stuff