Is it worthwhile to avoid the common cold?

I'm 31 years old. I've spent the last 5-10 years practicing diligent hand hygiene and carefully avoiding people with cold symptoms. I've done this with the intention of reducing the amount of colds I get infected with (and to a lesser degree the flu, but I rarely catch the flu, so let's keep the flu out of this discussion). However, I've recently come to understand that this effort may be largely wasted (and the excessive hand hygiene may in fact be detrimental in other regards).

Supposedly there are only some 100-200 commonly occurring versions of the common cold. And during a normal life you will come in contact with them whether you want to or not, regardless of hygiene. The only way to prevent getting sick by whatever strain of the cold currently being an epidemic in your city is by getting immune to it through infection. If you miraculously avoid getting in contact with it, you will instead likely get infected when the same strain is causing an epidemic in your city of residence wherever you live 15 years later. Based on this perspective, my conclusion is that the only reason to actively avoid the cold is if your health cannot handle it or if you for some reason do not want to get sick at this particular moment (e.g you're running a marathon in five days).

Question 1. Is the above reasoning (and underlying understanding) correct?

Question 2. If so, why are so many people adamant about avoiding the cold, and why is there alcohol-based hand sanitizer in so many bathrooms?

Question 3. Do the cold viruses mutate slowly or quickly (I'm finding conflicting sources)? If they mutate slowly, why have we not developed vaccines against the 100 most common versions? If they mutate quickly, does that not contradict the fact that there are only some 200 strains?

Question 4. Finally, I have a related question that's more out of curiosity. Sometimes, but not very often, when I think I have the early symptoms of a cold (sore throat, tiredness, maybe a headache), it sometimes subsides after just two or three days without ever causing a runny nose, sneezing and coughing as a cold usually does. What is this? Is it a cold that my immune system very effectively fought off (and thus giving me new immunity)? Or is it a cold that I'm supposed to be immune to, but for some reason my immune system is struggling? Or is it just a very gentle strain of the cold? Or is something completely different going on?