The largest downside is the rocket needs to be strong in more than one direction which adds a lot of weight. Sub Mach 1 first stage will save a little net weight but significantly less than you might diets assume.
Sure, but the strength it needs to have in the additional "hanging horizontal" orientation is only 1g -- much less than the many-g strength that all rockets need to have along their thrust axis. It adds some weight, but not enough to ruin the other benefits.