People believe this because every single member state is using EU institutions as a punching bag whenever they have issues locally. The people have no idea how the EU work, they only hear about it when used as a bogeyman
It also ignores the fact that absent the EU, countries would still have a lot of subsidies.
Edit: I just now got the part "If the increase in cake size is bigger than the subsidies" – that's a ridiculous assumption. EU total growth in 2025 was 1.5% or 295 billion USD. From 2021-2027, the EU budget committed roughly 370bn € each for Agriculture subsidies and for Cohesion Policies, totaling 720bn € over 7 years; 2025 has seen ~130bn USD from those two buckets alone. Germany alone has paid another 60bn in subsidies the same year. Oh, and there has been a total of 417bn USD in energy subsidies in europe in 2023 (most recent data available). Even if we could attribute all total growth to subsidies alone, we'd have a factor below 0.5 – and that doesn't include any growth through private investmen, PPP, or any kind of increase of regular public spending.
Futhermore, what matter is the amount of tax collected by the EU. Energy subsidy is not money collected by the EU and distributed.