Yes, I belive 1 LTC could be more worth than 1 bitcoin since price depends on prices of new coins and there are more BTC that LTC mined yet. BTC won't keep its 95% marketshare of crypto so that value will go to alternatives like litecoin.
Why do people seem to think that more mining power has an effect on price?
Price affects the number of miners and the network hashrate, not the other way around.
No, that's a far to simple view and it's a Sellers market.
More mining power of network means higher costs to mine. Miners are not willing to sell below what they belive it's worth and their cost of a new coin is a good indicator for value. Marginal costs are just a fraction of total cost so they keep mining and they rather keep them than selling at loss.
BTW: Markets can be very stupid for a very long time and from all markets I know bitcoin is among the stupidest so don't exept it to behave rational.