From a strictly legal standpoint, in the US (I'm also interested in Canada) can you (not should you) accept compensation to taxi an aircraft if you don't have a commercial pilot's license? If I was a mechanic with just a private license, could I charge for my time while taxiing an aircraft?
Yes, as per 61.113:
(a) Except as provided in paragraphs (b) through (h) of this section, no person who holds a private pilot certificate may act as pilot in command of an aircraft that is carrying passengers or property for compensation or hire; nor may that person, for compensation or hire, act as pilot in command of an aircraft.
A person taxiing an aircraft that is not intended for flight is not acting as PIC under this rule, and therefore can not only be a private pilot, but the person doesn't have to be a pilot at all.
There is no specific FAR that qualifies someone to taxi an aircraft, but aircraft operators and maintenance shops train and authorize mechanics to taxi and run-up engines.
Some individual airports have regulations that specify who may taxi and run-up an engine, such as Palm Springs:
(a) Only qualified persons shall start and/or operate an Aircraft engine at the Airport and/or taxi an Aircraft on the Airport. Qualified persons include a pilot, an airframe and power plant mechanic, or a qualified technician licensed by the FAA and qualified to start or operate the engine(s) and/or taxi that particular type and class of Aircraft.
14.20.130 - Who may taxi aircraft. No person other than a mechanic, pilot, or properly authorized student pilot, certified by the FAA, shall taxi aircraft on any part of the airport.
I would say yes you can as per the FAR as I read them the limitations on a PPL are
§61.113 (a) Except as provided in paragraphs (b) through (h) of this section, no person who holds a private pilot certificate may act as pilot in command of an aircraft that is carrying passengers or property for compensation or hire; nor may that person, for compensation or hire, act as pilot in command of an aircraft
So you cant act as Pilot In Command for hire or if there are passengers on board (which in this case I assume there are not) however if we look at the FAR for the official definition of "Pilot In Command" we will find
Pilot in command means the person who:
(1) Has final authority and responsibility for the operation and safety of the flight;
(2) Has been designated as pilot in command before or during the flight; and
(3) Holds the appropriate category, class, and type rating, if appropriate, for the conduct of the flight.
The question is does taxing count as a "Flight". I would think it does not and moving the aircraft around is part of maintenance (thats how they log the hours on the trainer planes I rent). The FAR definitions section (§1.1) does not seem to contain one for "flight" so that may be open to interpretation. But as I read it you can taxi the aircraft for compensation as its not a "Flight" and thus you are not the Pilot In Command which is when the PPL rules would come into play in my opinion.
However section §65.81 states
However, he may not supervise the maintenance, preventive maintenance, or alteration of, or approve and return to service, any aircraft or appliance, or part thereof, for which he is rated unless he has satisfactorily performed the work concerned at an earlier date.
The key line (Bolded) is return to service. If Taxing counts as returned to service then (unless rated to do so) you may not be able to for this reason (nothing to do with compensation).
Note: I am not a lawyer nor an aircraft mechanic and can not guarantee that my assumptions are correct. The opinions stated above should not be used as official legal advice and there may be more information in the FAR that I have not come across. This was compiled after some quick reading and searching in the assumed correct places.
Note 2: I would assume that in a commercial setting (and really any setting) there are some insurance implications to this kind of operation (especially with large aircraft). This may almost be a bigger concern than the legality of it (although both are important). You would not want to get into the situation where you may be legally allowed to drive the plane on the tarmac but are not covered by the company's insurance. Should you get into an accident you or your shop may become liable for the damages.