We know that because western ships aren't able to take this route successfully. Western ships either go around or they get attacked at which point they either end up being sunk or turn around. The impact is very visible https://www.spglobal.com/marketintelligence/en/mi/research-analysis/supply-chain-red-sea-shipping-disruptions-impact.html
Yemen doesn't need naval ships or planes. They have missiles and drones which is enough to cover the area. Meanwhile, even US military is now complaining that shooting multi million dollar missiles at thousand dollar drones is not practical. The whole US strategy is being invalidated by new technology. US navy is a dinosaur.