Might it be possible that a pulpectomy be performed from the side of a tooth rather than drilling through the crown?

Thru the crown: The best access to the pulp tissue is thru the crown of the tooth so this is the reason why we go thru the crown and not the side.

Entry: In a pulpectomy the entire pulp is removed. In order to gain access to the space, the normal entry point is through the biting surface of the tooth for posterior teeth or the lingual surface for anterior teeth. However, there are exceptions depending on the mouth opening ability or position of the tooth. A surgical root canal treatment is gained through the side of the tooth but also through bone.

Protocol: It is best recommended to do a pulpectomy and drill according to the standard of care and follow proper protocol that is research, proven and more predictable. Either from side or on top or anywhere the drilling occurs, you will have to have a restoration placed.

I Would Not: Predictable outcomes are what patients want more than anything else. If a doctor wants to "experiment" on a patient, there are protocols for that behavior and they must consent, in writing, to that "experimental procedure", to name a few of the necessary protocols. That said, performing a pulpotomy/ectomy via the buccal aspect is not established treatment, and in my humble opinion, shouldn't be.

Access: Yes. It is possible. The key is access. For example, if you have a front tooth with large facial decay, it is actually more conservative to gain access through existing opening than to drill through the back side (palatal) side of the tooth.