An interesting debate. I also would not remove my through hull log. In fact I go to a fair bit of bother keeping it working and accurate. However, I suppose it is probably the least useful and the most trouble of the basic instrumentation set-up of compass, depth and speed. I do like the near instantaneous info about speed and the double check of distance covered through the water when plotting positions etc. I do still plot fixes on the chart and I do still use a compass for fixes because I'm sad and like the intellectual exercise ... but I also use a GPS.
I recently sailed a Sweden 42 on "Blind Week" out of Southampton. This boat had a fully integrated electronics, plotter/radar package with amazing instrumentation and was superb to use. However, we still kept an hourly log and maintained a plot on paper charts too. I assume some of the data being integrated included input from a paddle wheel log since speed through the water was available. It was quite sobering doing a "what if the electronics go tits up exercise?" when navigating up the east coast of Alderney. I do worry about these boats with a fabulous plotter in front of the helmsman but no other fall-back navigation being done.
Would I fit another paddle wheel transducer? Probably not. I would however fit another instrument that gave speed through the water if someone would invent an effective, economic bit of kit that did not involve spinning drogues or paddle wheels.