A few facts (but don’t let this get in the way!).
TFR’s are “harsh”, pH 12+ and normally built with caustic soda actives or metasilicates that hydrolyse to caustic, both of which can be aggressive to paint and aluminium.
A properly formulated bike cleaner would be formulated sympathetically to above, employ alkalis that are known to be passivators, particularly for alloys and be safe in long term application. They’d also likely contain higher levels of surfactant and be better at breaking and lift dirt such as mud and grease.
Also remember the very high pH of TFR should not enter the surface water rain water drains post use.
As for the washing up liquid most if not all are viscosity modified with various levels of common salt – Sodium Chloride – which again will aggravate the potential for corrosion / oxidation – obviously red rust on ferrous iron or white oxides with un-lacquered aluminium.