I heard my name whispered.
Trees in raised garden beds, that's a big yes, can be done and the beds can be much smaller than you'd think. The roots of most trees including pretty much all fruit trees are relatively shallow. Young saplings start out with a tap root, but most trees as their root systems mature spread out to form a fibrous mat. The exceptions are trees like pines, elms, firs, walnut and some other edible nut trees that do maintain a significant tap root. Thus, fruit tree roots don't go very deep at all. One of the taller Birdies beds would be more than sufficient for a fussy avocado tree over clay soil, other less fussy fruit trees can do just as well in one of the short Birdies beds. And they don't have to be very wide either. My fruit trees did just fine in the smallest Birdies beds which are around 50cm wide, square. The roots just spread out until they reach the side of the bed, then they go down, and once they're below the bottom of the bed they start to spread sideways again.
Worst case scenario, after 20+ years the tree outgrows the garden bed, the bed has to be removed, but that's easy enough to deal with, just remove the bed and leave the mound of soil there like a little hill.
All my fruit trees (whilst they're dormant) are getting moved into large 50L pots for the sake of portability whilst I make some major changes around my yard. Half my trees have been in 50L pots for the past year already. They won't grow as large in a pot as they would in the ground, but they still grow well and bare plenty of fruit. Avo trees can be grown in pots, so there's no reason they won't do well in a raised garden bed so long as you have decent friable soil in there. Nothing special, just not too much clay not too much sand, the squeeze test Mark does and shows in many of his videos that mention soil quality is a good test.