Your question seems odd on the surface, but it's actually quite an interesting one, since few seem to know what nose hairs are good for.

My personal thoughts on this are just thoughts, and not based on any scientifical knowledge or long-term observations:

While nose hairs may be able to hold back ("filter out") a certain amount of bacteria and viruses, they are by no means dense enough to be able to do a thourough job of this.

From what I have seen from around the world, it seems that people in cooler climates have a lot more nose hair than you would find in tropical countries. What to make of this? In tropical regions they know colds and the flu as well, so I don't think there's a relation.

My dog has no visible hair inside his nose, but he is also as prone to colds and types of flus as humans. But his body temperature is higher than ours; about two degrees celsius. At the same time, his fur is dense and quite a good protection against cold weather and, to a certain degree, heat. Again, what to make of this? Is our nose hair simply here to soften the sting of the cold air during winter? To help against hypothermia? Seems farfetched, but I think it possible.

My superficial conclusion is this: in our times, nose hair does not serve any type of protection anymore. If it ever did, than our vastly improved living conditions do not require them anymore.

As I said above, these are just some quick thoughts, because I found your question really intriguing.

Nose hairs do filter out a certain amount of dust, bacteria and such but they are not a total necessity...so if they fell out, no big deal.

I have the same problem. Have you found a way how to regrow the hair? I am really worried about this condition. Sometimes when I remove my booger it has some blood. 😭

I actually read an article cautioning people not to trim their nose hairs because they do indeed filter out foreign substances. You can't see a lot of them as they are too fine - these actually aren't even called hair, but cilia (?) or something similar to that. I imagine yours will grow back, however, and if it's just the ones at the bottom of the entrance to your nose, you have others.
I thought I had lost mine, too, but turns out the flukes in there had just covered them up with that white liquid they blow out that looks like skin when it dries. lol