Why wasn't it designed into Typhoon? Because no-one thought that there'd be any prospect of the RN operating CTOL carriers again, the Germans, Italians and Spanish had never operated CTOL carriers and weren't planning to do so, and the only likely candidates for a future CTOL carrier aircraft were:
1. The French - who would build their own
2. The Soviets - ditto above
3. The US - ditto above.
4. The Indians - who, it was assumed, would either go down the STOVL route in future (because of their SHARs), or if they did decide upon a CTOL carrier in the future, they'd buy from the USSR or the French (or, at a considerable push, the US).
With hindsight, we (the UK) ought to have invited the Germans, Italians and Spanish to shove off/consider buying the F-16 or F/A-18, and accepted that by teaming up with the French (after explaining in words of one syllable to Marcel Dassault that 'bi-lateral collaboration' didn't mean Dassault having about 90% of the workshare and profits) and accepting a latent CTOL carrier capability we'd be keeping our options wide open, even if it seemed improbable that we'd ever go back to that sort of carrier operation.
The problem was that we didn't trust Dassault an inch after the various shenanigans with Jaguar exports; we didn't entirely trust the French (years of history and the AFVG experience) and we were used to working with the (West) Germans and Italians via Panavia. On top of that, a bi-lateral with France wasn't going to help the then-Sec of State for Defence's ambitions to become PM as well as a quadrilateral arrangement (how did that plan work out for you, Lord Hestletine?) and we weren't going to return to the days of having a CTOL carrier - and STOBAR was (at the time) the concept of a few dangerous loons who didn't understand the nuances of carrier operations.