Yes, people can jump. Bunny hopping isn't the same as jumping. Consecutive jumps are not possible without significant slowdown. There is no way to retain momentum, so it's not even close to bunny hopping. If you need to understand what bunny hopping actually is, just take a look at how people do it in Counterstrike GO.
https://youtu.be/mgnECvX3nnc?si=fgVUiHBX45qd7c-1
A and D are just basic movement keys. You can certainly repeatedly move left to right, but you can't spam it. The movement simply isn't fast enough. It also penalizes you in multiple ways.
You make it sound like even the most basic movement in Battlefield is an issue, but it simply isn't. The issue is the way DMRs are balanced. They have abysmal damage per minute, high recoil and slow recoil decrease.
People have already made spreadsheets with TTK calculations and DMRs are pretty much at the bottom of the list with 400 ms+ TTK while most other weapons are below 250 ms.