You have a potential issue. HFT is where I would start. Kit can be normal to compete to a decent level. However... course setters make course that are designed to test the tall and the short...young and old...left and right etc. Targets are often placed to test the shooter...forcing a low shot..a stretched shot...kneeling crouched...partially obscured in height or left to right.
With a chair you will probably be more restricted re heigt adjustments so the course setter has to either factor a shooter at one potential height at rope end ....I see that as being a difficult stroke to pull off when they also have to make a course for tall short young old fit knackered .... well younget the idea.
It may be possible for the setter...course captn and marshalls to allow dispensation to allow for the shooter to shott from a position where they have some sort of line to target but hellish to say the least and not really a level playing field.

Also....A lot of HFT and FT courses can get very very muddy and I think any form of wheeled transport may really struggle unless methods are employed to address this.

There are courses Inhave shot at where you come off looking like a strawberry half dipped in chocolate....
This is potentially a difficult thing to pull off for all parties.
Doesnt mean it cant be done but its going to be a shit steep learning curve for sure.