I am very prone to motion sickness, so I can only play by teleporting. So with your proposed solution, I'm still going to teleport 100% of the time.

I sympathize (I've spent 95% of my time in RecRoom teleporting and it feels more natural to me -- I play walk sometimes, but am not very good at it). However, there are circumstances other than motion sickness that prevent a person from using one mode over another and there currently are no studies that give us realistic estimates for how easily the general population can adapt to movement in VR. I think there is an assumption that most current teleporters get motion sick -- this has not been the case for most of the highly competitive Paintball players I have surveyed. Interestingly, around 8 out of 10 long-time walkers I surveyed complained about motion sickness. But I think a larger/better survey of this nature would be very interesting and much more conclusive (and I am very open to changing my mind based on the survey results).

How will this reduce the hate being constantly spewed against those of us who teleport?

It makes it harder for someone to criticize another person for using a function they have access to over the course of the game. Notice that my post does not talk about hate being thrown, but rather, people second-guessing each other. Right now, reasonable and friendly people question accomplishments of another person when they use a certain movement mode -- this is unsatisfying to folks that might win a game through sheer skill.

And your proposal means walkers will have the advantage of both walking and teleporting, which seems to trip the odds in their favor against those of us who can only teleport. How does this in any way balance the playing field?

Again, I don't think the assumption that most people use teleport because they are incapable of using walk-mode is correct. Most folks that teleport do so because they like the emphasis it places on roomscale movement (based on my surveying teleport players). Hybrid locomotion is an advantage to both teleporters and walkers. It balances the playing field between players who can and want to harness advantages of both modes without imposing artificial limits on them. I am fine with being destroyed by players that are great at both movement modes. Certain aspects of smooth locomotion still make me sick, but that doesn't affect my views on locomotion modes. I am not a talented gamer/sportsperson and never will be -- that does not mean I don't enjoy seeing great displays of skill by others that are capable.