Insulted by supply jibes
In my experience, supply primary teachers are focused on pupils' learning needs. They do their best, subject to the quality of the planning supplied to them (often within minutes of the start of the school day), to offer pupils an appropriate and enjoyable learning experience which builds on previous lessons, and adds to their knowledge.
Afterwards, they habitually leave notes to inform the next teacher of what they have covered in the lessons.
My fear is that, in future, classroom assistants may indeed be employed as (to quote Sir Bob's words) "the gap fillers" (who) are ... child-minders with little interest in high-quality teaching".
The deployment of staff who are not qualified teachers to teach classes sends the message that the qualification is unnecessary. This will undermine the morale of qualified teachers, both in permanent employment, and teaching "on supply".
Qualified teachers may indeed see "the advanced classroom assistant ... as a cut-price alternative", a crude means of depressing the already low remuneration available to professionally qualified staff who, unlike their support staff, have foregone five or six years of pay to achieve their professional qualification.
To return to your headline, yes, teachers should teach, and teaching assistants should continue to do the job they are expert at, assisting the teacher.
33 Swinton Rise