Actually Bitcoin price often influence altcoin price but there's a season where altcoin do extremely well even when Bitcoin is stagnant or declining.
In my experience, there has never been a season as you said, bitcoin will always be the first coin to increase in price and drag the entire altcoin market up with it. Bitcoin is like the soul of the crypto industry, and everything only works well when bitcoin works well.
What if this season comes More often, what will be the faith of Bitcoin?
But if there is a season where altcoins outperform bitcoin, it is unlikely to cause investors to lose faith in bitcoin. Because at the end of the day, altcoin hype is temporary and will end at some point and everyone knows it.
People trust bitcoin not only because of its profits but also because of its decentralized nature, use cases...and so far it is the only trustworthy decentralized currency. So it is difficult to shake the confidence of bitcoin investors in the long term.