Recently removed carpet from stairs and found pine treads & risers. Would like to replace with solid oak. Tearing out the old treads & risers seems like a lot of work, so we're planning to just remove the "lip" of each tread, and then glue and nail the new treads and risers over the old. There shouldn't be much noticeable height difference in the first & last step, since the floor is already raised with hardwood plank flooring. Does anyone see a problem with this?

Sounds like a plan to me.

Should work out OK, as long as you have it figured out with the height.

Most hardwood plank flooring (solid) is 3/4" thick. Most solid stair treads are 1&1/16" thick. This will affect the "rise" of your stairs. You could successfully use flooring for your stairs and this would keep your "rise" all the same.