" as we move to 3G, 4g and 5G, the cells will be much smaller and more towers will be needed"
First there was GSM at 900MHz (Cellnet, Vodafone).
Then there was PCN at 1800MHz (Orange, One2One). Being twice the frequency, 1800MHz needed lots more masts than 900MHz did to achieve similar levels of coverage.
Then along came widespread adoption and expectations of near-universal coverage. Suddenly "masts" popped up in all kinds of places - high streets, petrol station chains (yes), and more. You wouldn't know these existed, but without them the networks would have neither the coverage nor the capacity.
Then there was 3G, and as 4G allegedly came along some operators let their 3G networks dwindle.
I'm not at all convinced that the poor overall coverage is due in any significant way to masts sited in the wrong place.
I am rather more convinced that there is no visible financial motivation for networks to improve their existing coverage.
In passing: why isn't cross-network roaming an option for customers of the UK majors. It already works for visitors from overseas, and is already offered by a tiny handful of tiny UK operators too e.g. Anywhere SIM.