You really need to stop conflating aircraft with rockets. It's embarrassing.
That's not really the issue, actually. Some smaller rockets can (and sometimes are) launched this way and there's been interest in scaling it up for a number of years. Concepts for exactly this sort of launch system date back to at least the 1970s with exactly this same logic behind them. Without exception, they all ran into the wall of the feasibility issue, getting a small enough rocket or cluster of rockets to actually lift the main booster with enough time for the thing to orient vertically for the ascent phase. The best concept I ever saw involved using a two pairs of very large SRBs with 90-degree angled nozzles for a rapid ascent to about 600 feet before the engines separate and the rocket ascends. The real problem with the design proposal, ironically, was that the physical structure of the rocket would have trouble standing up to the lateral forces of the launch; rockets are usually designed for strength along their long axis, and designing along two axises is going to cost you in terms of weight.