You get diminishing returns as you increase the rank, so with a fixed training budget it's not clear whether you get the best return from increasing rank vs increasing something else. If you start off by training DynLORA with max rank 8 you can see returns diminish fast beyond rank 5. Then you can use rank 5 for the rest of your training. You wouldn't know that with LoRA. I think this is the idea behind the paper. If you are just going to use your entire budget training a DyLoRA with max rank 8 then you're right there's no advantage over LoRA with rank 8. You'd have to use the ability to assess multiple ranks in order to see some benefit.

Why is the only advantage at training time? I might misunderstand something but with this method you can train once, and then deploy models that use arbitrary rank (according to end-users compute requirements) and expect to have a model that performs best for that specific rank.