There is a market case for a new trainer. Making it single-engined is commercially and operationally sensible.
The market is mixed bag. Airbus says there is a market for 300-500 aircraft - this seems tiny compared to the hundred of turboprop trainers that have been sold and the over 1,000 Hawks built alone. Even if Spain and France brought the AJFT that's probably no more than 50-60 aircraft combined, hardly a profitable return.
So far Alenia Aermacchi/Leonardo have managed to export 72 trainers (Israel (part of deal for AEW equipment and recon satellites), Poland, Singapore, Azerbaijan, Turkmeninstan). Far more KAI T-50s have been built, over 200 but of which only 64 were for export (Indonesia, Iraq, Philippines, Thailand). In Israel, Poland and Singapore (and the UAE but they subsequently put out to tender again with no result so far) the T-50 lost out to the M-346 - which rather belies your claim that the M-346 is inferior to the T-50.
The T-7 is still early to estimate, it well be under US Congress export approvals so that will limit some buyers. Hawk hasn't shifted any exports since 2017 and isn't likely to now.
What is clear is that KAI is very strong in the Asian market and with Pakistan, Spain and UAE with possible users gives a chance of a global breakout and the FA-50 offers a greater lightweight fighter option for smaller nations. Leonardo hasn't made much market impact. But most of the M-346 and T-50 users so far have been second-tier and third-tier airforces. All the major airforces have so far concentrated on replacing their turboprop basic/advanced trainers.
Pilatus has shifted 235 export PC-21s (Australia, France, Jordan, Qatar, Saudi Arabia, Singapore, Spain, Switzerland (as a Hawk replacement), UAE and 2 for Qinetiq in the UK). I won't list all the T-6 Texan II and Super Tucano sales but they top over 500 together, so there is no doubt that up until now propeller-driven trainers have far outstripped the exports of jet trainers (750+ vs. 136).
This won't continue forever, at some point the market will swing as new LIFT are needed from the 2030s onwards. The question is how many airforces will want a supersonic LIFT? Some may try and bridge PC-21 to frontline jet, others will want a jet to slot into that. A highly agile airframe is a must but I'm not sure that supersonic performance brings you vastly more benefits and - so far - we haven't seen air forces queueing up to buy them. Also remember that increasingly Western training is being contracted out to private industry, how many of them are going to want to pick up supersonic hardware that is costly to maintain and increase the price of their bids?
I feel the answer will be a mix of supersonic and subsonic/transonic but leaping into the unknown with a fresh design now with component trainers still is a hard business decision to make. Both M-346 and T-50 have origins back to 1992 and for 30 years of development and sales work they have amassed around 300 aircraft - not a very great return. EADS jumped ship with Meko, they didn't even attempt to battle it out with the Hawk or M-346. It's also interesting that we've never seen a home-grown trainer from the US industry - T-6 Texan II builds heavily on Pilatus expertise and even Boeing had to team up with SAAB to get a 'home' product.
Apart from Qatar, and Saudi Arabia, you mean? The trend has been very much towards multi-platform deals, and trying to keep other manufacturers out of your most lucrative markets. I'm sorry to use the word "clearly", but it really is blindingly obvious that if you can, you'll supply as much of a customer nation's requirements as you can. And from a customer point of view, it tends to make support and sustainment easier.
I'd love you to give some examples because I can't think of many (no I'm not counting Al-Yamamah as that was 30 years ago) beyond the last few Hawk LIFTs to Saudi Arabia and Qatar (who also have PC-21s and Rafales in their fleet). Airbus and Dassault had no trainers to offer with its Typhoons and Rafales and F-16 operators use a wide range of trainers, I've never seen many references to package deals (not really sure the Hawk 200 counts either).