- Hanging under-wing is a totally different set of forces than standing vertically, especially for a big rocket with thin walls. You're more like a bridge than a tower, or rather like a bridge one moment and then a tower the next. You need reinforcement for that, which makes the vehicle heavier.
- Modern reusable rockets do quick "load and go" filling to keep their propellant as cold and dense as possible. You can't do that if you need to fuel on the ground and then hang off an airplane for ~an hour while it climbs.
There's no future in this idea outside of small sat, and probably not even there.
But that's how a lot of the X projects were / are done.