I'm F-1 and I haven't applied for TPS/EAD but my wife (F-2) did and we let my DSO know about it. From what the DSO, the attorneys that DSO consulted with, and an attorney I talked to said:
F-1 students can apply TPS or TPS + EAD. They are still in F-1 status as long as they continue to follow the rules of F-1 i.e. you are still required to maintain good academic standing and limited to 20hrs per week on campus job. TPS EAD will allow a F-1 to work anywhere they can find a job, but that will violate the terms of F-1 and therefore, the student loses F-1 status. And if the student wants to return back to F-1 after some time or when TPS expires, they will have to go outside of the country and apply for new F-1 visa, just like the first time.

If you let DSO know that you're going to work off campus using TPS EAD, they'll most likely terminate your F-1. If you don't let them know but still work off campus on TPS EAD, it's illegal and may cause issues down the road..for example when you apply for permanent residency or your DSO might find out about it and terminate your F-1.

So it has both benefits and risks/limitations. Just be careful and consider the risks vs benefits before jumping on the TPS bandwagon. If you really think TPS might help you, apply for TPS without EAD for now and apply for EAD later when you need it.