Instead of L15,why not j10?
Because:
- J-10 is not a proper trainer aircraft (of which the JL-10 is), but an actual fighter jet.
- The inherent design of the J-10 means that there's actually more cons than pros to navalize it (as the criteria for carrier-based fighters are actually more stringent and demanding than land-based fighters).
The choice of YF-17 over YF-16 for the USN's VFAX program (where the YF-17 eventually becomes the F/A-18) explains a lot.
Relating to the fighter jet matter, it should be noted the J-10's weight class is that of a medium weight 4th generation fighter in the class of say, F-16.
There are some single engine lightweight trainers that can also be developed or have variants as light fighters (or vice versa), such as T-50/FA-50 and even the JF-17 and LCA Tejas and Gripen B/D could in theory could be developed into dedicated trainers, as they're all in a similar weight class. Similar to the T-7. They're all powered by a single engine of the F404 or RD93 thrust class.
J-10 is in a heavier weight class, powered by a WS-10/Al-31/F100/F110 class engine.
L-15/JL-10 is in a similar weight class to the likes of T-50 or T-7 (or indeed M346, Yak-130). Similar to M346 and Yak-130 it is twin engined, which offers some benefits for aircraft ability to sustain flight and overall redundancy, if one engine fails. For naval purposes that is particularly beneficial.
This isn't to say that naval aircraft cannot be single engined (F-35, A-4 and the T-45 Goshawk naval trainer for example are all highly successful), but it does offer a degree of less redundancy than a twin engine aircraft.
So really developing L-15/JL-10 as the naval trainer of choice makes a fair bit of sense.