I bought a “Variera” pot lid organizer, extended it to the max and attached it to my heater wires with plastic cable ties. That required no drilling and absolutely nothing else. It’s now holding my bathroom towels.
And here is the original use for the variera.
Regarding the variera I believe that this objects can give birth to hundreds of other objects. Just like anything else.
No need to use too many plastic lockers to fix it to the wall, towels aren’t too heavy and plastic is strong. I used 4 for mine. Enough.