The main issue in this regard with the crypto market is that the only channel to investing is through FIAT such as USD.
No, I'm having enough services to invest into cryptos with my local fiats and I'm not completely depending on USD hence it means I'm not depending on US economy with the respect to crypto investments at least.
If there's an economic crash in the US and people try to cut their investments then there will be less dollars to flow in to crypto.
Again you are wrong, when there will be a crash in US, then there will be more money flow into crypto but you're stating people will cut. Because, people will not invest into US based stocks but they will look for other investment opportunities.
Within crypto there would likely be no the same struggles, that's why low cap alts that only seem to trade BTC/alt don't have too much fluctuation in times like this.
Those lowcap markets are not fluctuating due to various reasons, one of them must be due to lack of new investors but it is very loosely tied but the downfall of crypto market as you have mentioned. There are altccoins which are performing well even entire crypto market was falling down, good example in recent times is waves.