Front landing gear disagrees with you.
I fail to see how it's also designed for carrier ops, as there are no carrier designs for it to land yet. This is made by TAI's own resources. Their goal is to create a LIFT trainer for hvkk and even that is not yet guaranteed. Let's not get that ahead of ourselves.
If Hürjet becomes a reality and an N version is in the works, it'll be buffed up heavily in structural integrity and MTOW will increase. Probably will need 2 engines or a bigger one. As it currently stands with the F404, not worth to have her on a carrier, what good will it do?
Indian Navy rejected Naval Tejas with F404 due to bulked up increased MTOW which limits the radius and weapons capacity. It also finished landing and take off tests from aircraft carriers. From the results, Navy also rejected F414 engine upgrade seeing it still would carry low capacity and wanted multi engine aircraft.
IN requirement is different. It needs to police last swathes of water. So it needs an fighter with long legs. But Turkey can make do with an fighter with shorter legs as it’s primary threats are not far away. Hurjet in Naval role may still work.
However I agree, turning an Air Force variant into Naval variant is time consuming, complex design changes etc