Always happen to enlighten! Yes, miners support network security, but that is a cost of entry that is not factored into the exchange rate of a coin. If a coin is being mined and bought, then it is viable (i.e., worth something). If a coin is not being mined and bought, then it is not viable (i.e., worth nothing). This binary switch of making a coin worth something greater than zero is the ONLY positive impact miners can have on the value of a coin. I explain:

Miners exert downward pressure on the value of a coin in two significant ways. First, miners are necessarily inflationary to a coin. No matter how many of the coin they buy, they will always have more for sale by virtue of the fact that some proportion of their holdings have been essentially plucked out of the thin, blue sky. Second, miners are also necessarily more likely to dump a coin because their investment is associated with a lower cost of acquisition. Therefore, they can still profit by selling the coin at below market values, driving exchanges rates downward.

So, in other words, miners contribute to the difference between 0 and >0. After that, their influence is entirely negative on a coin - investors and only investors are responsible for any subsequent increases in exchange rate.