Actually Bitcoin price often influence altcoin price but there's a season where altcoin do extremely well even when Bitcoin is stagnant or declining. What if this season comes More often, what will be the faith of Bitcoin?
Bitcoin has a huge effect on the market especially the crypto market and as a result of this the volatility of bitcoin actually affects that of other crypto currencies. The volume of bitcoin and it's market cap contributes to how strong the general market trend is being it a buy or a sell. Based on your assumption if bitcoin was present and not moving either to the upside or downside, then momentum in the market will slow down. But if bitcoin isn't present for instance then the market will depend indirectly on the next highest currency at the time and it's effect will also depend on adoption and market volume.