Every single model reviewed by SAGE has predicted a summer wave which included the rise in (i) cases, (ii) hospitalisations and (iii) deaths. We might have got away with a different outcome in the pre-Delta world but, unfortunately, it is no longer an option.
I do not think any of regular posters claimed that "cases do not matter at all" or "hospitalisations will remain in low hundreds", etc. Of course, cases eventually lead to hospital admissions and hospital admissions sadly lead to deaths. The percentages may be lower (i.e. fewer people will end up in hospitals and fewer people die) but the link will still exit.
The big question is the size of the wave and this is where we are dealing with a wide range of unknowns.
For now it looks like we are running closest to models developed by (i) LSHTM and (ii) James Ward (a mathematician on twitter who appears to have learnt a lot about infectious diseases since the start of pandemic).