It depends whether you believe immigration is the cause of those problems. To answer your points (all valid ones I may add):
(a) There are actually enough empty houses to house everyone, plus the sell-off of council houses and refusal to replace those, so that working people can have affordable housing.
(b) We aren't training enough doctors, and we aren't paying those that we have trained a decent wage commensurate with their value and experience. We are reliant on immigration to make up the numbers.
(c) Connected to (b). If we could get to see GP's easier or have more walk-in centres for minor ailments, the pressure would be off A&E departments, which are the first call now for many.
(d) There will always be better and worse schools. And even without immigration, the population would be growing. We don't do joined-up, forward thinking in government. It's all knee-jerk, short-termism these days.
(e) Austerity imposed in 2010 has caused many of the problems above. And while QE mitigated the worst of the financial crisis, we probably should have eased off earlier than we did. And then there was Covid. A lot of the problems are due to profiteering and privatisation. Energy companies making fortunes, utility companies ripping us off, water companies borrowing vast sums that, instead of investing in infrastructure, they paid out in dividends.
(f) See above. Also the decision to pay the WFA to anyone of pension age was probably a flawed one in the first place.
(g) People use this phrase "illegal immigration" without understanding that legal migration completely dwarves truly illegal immigration. People who are refugees from violent situations or seeking asylum for other reasons aren't "illegal".
And many industries, particularly in the health and social care sectors, rely on immigration. It's simply not logical to say that we should stop immigration while complaining about the lack of doctors and dentists. No one could argue against securing our borders, and making sure we know who's here. But the free movement of people as part of EU membership played a huge part. Leaving the EU reduced that significantly but it also encouraged illegal migration via small boats.
