Can a DTV visa holder based on Thai children maintain a work permit in Thailand?

Surprisingly this comes up quite a bit

There is no DTV (Destination Thailand Visa) category where having a thai wife or thai children here make any difference in getting the visa.

and

there is also no category where you can legally work inside the country for a thai company, get paid here or hold a work permit..

You either keep getting 90 day single entry Non-O's along with the one 60 day visit family extension you're allowed (which gives you 5 months total)

OR

you become the legal father of your thai child (get parental rights granted thru family court decree or by the Amphur if the child is old enough) and apply for a yearly extension.

That category where you see Spouse / Children is for foreign spouses or children of a primary DTV holder not for anyone married to a thai or having thai children. ..