I don't think scrapping the skills tests are the way forwards- although I do know a few people who live in rural areas who had to travel a long way to sit them- which is a PITA. Perhaps having more test centers and making it possible to sit the tests outside of Monday-Friday 9-5 would be a good idea?
I do sort of think the tests are neither here nor there (I passed them first time) but I'm also not sure someone who can't pass them would make a good teacher. They're just a hoop to jump through- and you can practice for them and there are some great YouTube videos available online. FWIW, I think the timed element of the maths test is worthwhile, because as a teacher you do have to be able to respond to children's questions quickly and under pressure!
I'm not sure making the PGCE easier to get onto is any sort of answer to the teaching recruitment/retention crisis. As someone who's just finished their PGCE, it's a bloody hard year- making it easier to get onto won't mean more people will finish it, necessarily. The drop out rate in my subject at my uni was about 25%, and I know from an NQT who'd been through the same PGCE, around 20% of her cohort had dropped out of their NQT years by Christmas.
I think there are really deep problems with teacher training that are linked to more general problems in teaching:
-Less schools (in shortage subjects at least) have full departments, so schools are less able to take trainees. This leads to trainees having insane commutes to placements/less suitable placements, which can be a contributory factor in them dropping out.
-Less experienced teachers are staying in schools, so in school mentors sometimes have less experienced and are less well equipped to support trainees. A lot of people I know had in school mentors who were say NQT + 2 and mentoring for the first time- this isn't a problem as such, but I do think having a good/bad mentor can make or break a placement for some people.
-If teachers you are working with are busy/stressed out, they obviously have less time to support you as a student- which means less good quality training.
-If you're in a busy/stressed out department, that's not a nice environment to train in, and it may put you off teaching.
-If you're seeing the problems in the profession first hand, this can obviously put people off wanting to be in the profession long term.
I'm not saying that the PGCE year should be made easier as such, but making it easier to get onto the PGCE won't necessarily help more people finish the PGCE, and long term won't produce more teachers. The fundamental problems in schools need to be addressed, and this will make teaching more attractive, and then there will be more new people coming into the profession.
I think the big crisis coming up for schools is also not getting a warm body in front of a class, but about who will be the future middle leaders and SLT in schools. If very few new recruits are staying in the profession for 5 years or more, it's hard to know where these will come from.