I think this problem can afflict a lot of older vehicles particularly depending on how they have been used i.e. lots of miles about the city, stop start/on, off etc, vs lots of long distance miles, so my thinking would be yes, but is it practical? A new swtch may be expensive and may be a bit of a chore to fit, not too sure having never done it.
I do know that the relay idea does work as a relatively cheap and easy solution and have used it to solve voltage drop problems in several old cars, I have previously owned a string of old 6 volt VW Beetles in years gone by, a different version of the same problem, but, the relays activation coil current draw is extremely low and it takes a large percentage of your switching current problems away, I know I said it is not a proper fix but it is what I do to overcome the issue, a "purist" would require a new switch to keep things as original, I just want things to work.............. your choice?.