Bath overflow etc

My bath and sink overflows are an obvious source of cold draughts when its cold outside, also the potholes themselves, slightly more surprisingly. What’s the view on these from a position of aiming for improved airtightness? If there were 4 one-inch holes in my bathroom wall i’d certainly want to do something about them. Are overflows really needed? Is the heat loss significant? Can anything be done to minimise the heat loss?

All my overflows just bypass the plug and return to the drain before the S bend, so air leakage is minimal, if any.

In terms of heat loss, if your waste water pipe goes straight out of the wall you could route then internally and out through the ground. Clearly a lot of work for potentially little gain, depending on your current heat loss.
If you wanted to get in to the detail, PHPP v10 includes an option to calculate pipe losses like these. It’s a fair bit of study and work, but accurate.

Bath and sink overflows are usually plumbed internally. But toilet cisterns and header tanks overflow externally to be observed, indicating attention is needed. Some toilet overflows are fed into the flush pipe to be observed in the bowl. I don’t know about header tanks though, however these are becoming scarce after the introduction of pressurised central heating systems.