From my searching for a hitch that could tow AND also take a bike rack, you need to carefully read ALL the instructions, both for use and mounting, of the hitch, the rack, and any other components. All reputable hitch makers and bike rack makers have them posted online. If they do not, I would pass on that brand. Inside adapters may not be authorized by one or the other (hitch or rack makers) or both due to often being too short, which allows a certain amount of rock unless very tightly fitted. Such rocking could also expand the adapter making remove difficult or impossible even without considing rust and dirt. The longer the interior adapter, the better as it spreads out the support and limit rocking, but still may be prohibited. (NOTE: this is not illegal, it is just they they will not warrant the adverse effects or damage it causes.)
Some hitches will say in the mounting instruction that they are NOT for hitch mounted bike racks unless the upper mount of the rack uses a strap to support the rack from bouncing. This is common for low visibility hitches that hide behind the lower valence. For me this was the killer as an upper support strap would damage the spoiler over the hatch that includes the high mount 3rd brake light and rear washer nozzle. I also did not want to cut the valence.
My sister has also encountered issues with carrying her bike on a rack where some bridges will not permit exterior bike racks in high winds (Chesapeake Bay Bridge) along with trailers of roof pods or racks.