Would it be a big safety concern to conduct a Battalion-sized FTX without Vehicle Recovery assets?

What does the Concept of Support in the OPORD for the FTX state? Dependent upon your type of BN, the FSB, BSB, or SBDE will have recovery assets in which you may request support. You will have to link up with their S&R NCOIC to formally coordinate those assets. Like vehicle recovery is the preferred method as that is what training for combat entails. As for recovery assets themselves, a heavy BN will have M88A1/A2 for Brads and Abrams. Light BNs will use wreckers. I am used to maintenance and recovery being an afterthought so, if it's not in the OPORD, make it happen.

Depending on terrain and driver's training you may be able to get away without wreckers, but you should really evaluate if you can safely use towbars at a minimum.

When I was mech Infantry we always had recovery assets when we went to the field for our Brads, MATVs MAXXPROs, etc. Sure, we could do some level self-recovery (sometimes), but we always had wreckers. Today, in my Reserve trans unit, even when we leave to exercise the trucks or get fuel we have recovery capability, to include the ability to call a wrecker if needed; and certainly when we drive across the country! That may not rise to the level of a "safety concern" per se, but in planning, I can't even conceive of why you'd go to the field without recovery assets available, but all experiences vary.