Tom,
Unfortunately looks and manoueverability are only a small part of the equation for whether a fighter is suitable for carrier ops or not.
Just look at the JSF, there are 3 variants, a CTOL (A), VSTOL (B), and Carrier version (C). Each one is essentially a different aircraft, with different underlying structure. The A version would never be able to land on a carrier, it's not strong enough and doesn't have the control capabilities of the C. A and C don't have the cool air vertical fan of the B, so they have a different structure there instead rather than a hole where the engine would go. The C's nose wheel opens in the opposite direction to the A and B, CAT shots would fold the nose wheel up on the A and B. The C has a larger wing and larger control surfaces. The differences just go on and on.
The Rafale was designed for carrier ops, the Typhoon never was. To make the Typhoon carrier capable would involve a complete redesign. A stronger undercarriage would only mean the aircraft breaks where the stronger undercarriage ends. So you beef up it's attachment points, then it snaps at where the attachment points join the aircraft. So you beef them up, it then snaps where you stop the previous beef up and it continues until you've redesigned the internal structure. But beefing up the internal structure takes up more space, then you find that the systems can no longer fit, so the systems need a redesign...it carries on ad nauseum. Never mind the arresting hook and the required structure to withstand multiple arrested landings. The loads involved in a carrier landing are greater than those generated by using the arrester gear at the end of a runway in an emergency.
Nothing in engineering is a simple fix or modification
