Always Helpful
It is always helpful to renew EAD. Here is my thought.
Since you are NOT using EAD for employment, technically u don't need EAD. But for following reason, it is recommended to renew EAD.
1. If something goes wrong with current JOB (leave / RIF) your H1 will be immediately inactive, but if you have EAD it is easier for you to look for another job.
Plus having EAD does not automatically gets you in 'AOS' status. You will still be maintaining ur status.
Along with EAD, also apply for AP.