I flew basic economy a couple times recently and had no problem using a small backpack as my ONE "personal item". The smallest, boots but not much else sized boot bag would fit. As long as it fits under the seat you're good. And, even with a full regular business or economy fare they can still make you gate check your 2nd overhead sized carry on when the flight is full and you are boarding late. First class or tiny, under the seat sized carry on is the only way to 100% guarantee you won't have to check your boot bag these days, albeit that risk is low, but possible.