One doesn't weld bikes, one welds metal, and each metal may have some different characteristics. In general though, welding does not harm tubing/metal within it's design parameters. Meaning the tubing is configured and sized in order to have the required strength post weld. Some tubings make use of air hardening steels to improve the post weld strength of the tubing (something I don't really think is necessary or likely to roll out with consistency). Aircraft culture is big on mildly post heating tubing in order reduce undesired hardening. This does not seem to be necessary within the parameters of bike welding.
The designed for success stuff applies to brazed or lugged joints also. While parent metal is not melted in those processes, the heating is elevated and prolonged, compared to TIG. This isn't ideal either. The take-away is that any of the processes have a list of benefits that can be hyped or disparaged. They all work.
PS Some of the "problems" with heat affects you are referring to are mostly related to the welding of heat treated metal. For instance if you are trying to weld a threaded rod section to a Bowie knife blade in the fabrication of the tang, it can be near to impossible to do this without affecting blade temper, and the weld can cause the high carbon steel side of the tang to develop hardness that will later fail in hard use. It doesn't appear to be a preferred option to attach the threaded section before the blade is forged/heat treated, because, possibly the threads would loose definition. This is an example where silver braze can come to the rescue. It will join metals of dissimilar carbon composition, without elevating the hardness during soldering , or with due care, drawing the precious temper. While obviously heat treated metals are not the only ones affected in the zone, that is often the kind of problem I hear welding trained guys worried about even when there isn't cause. In short, relax!