Raised beds over ground with aggressive shrubs. Doomed to failure without full root removal?

My question for the permie world is this: If I create three foot high raised beds over an area that has been cleared to ground level of aggressive shrubs and small trees (but not tilled) will the existing root systems die or sprout? In other words, how necessary is it to remove established root systems beneath a new raised bed?

I am working by hand and dealing mostly with red osier dogwood, alder, snowberry, and nine bark: all seem to be tenacious spreaders who laugh at mere cutting. I’m hoping that depriving them of light by covering with enough humus will quell the lust for life, but don’t want to go to the trouble of building extensive beds only to find they laugh at three (or more?) feet of earth, too. Do I need to get out the Pulaski and digging bar? Thanks!

To me, it seems wise to dig out the main root ball as much as possible. The smaller feeder roots are less likely to survive and sucker without the mother.

If you're working with a small area, it's probably worth it to go for removing as much of their roots as you can. If it's larger, maybe just go for the main root systems. It is certainly possible they may send up some suckers. If it's any reassurance, I have found that even if you miss some and they do sprout, if you just cut them as soon as you see them (especially before they can start photosynthesizing) they'll exhaust their energy reserves and perish. It might take a couple rounds of cutting back. For what it's worth, I've been using this method with Japanese knotweed and find it way easier than trying to dig every last bit. It's just another weeding task for me, basically.

I built raised beds over Japanese knotweed, it would often come up in the beds and they kids and I would enjoy pulling it out. The loose soil in the beds made it so when pulled the knotweed snapped 12” deep at the original soil line and a long piece was removed. This happened less and less each year.

Thank you for the responses, much appreciated! Sounds wise to do as much removal as possible, sigh. To the roots I go!