Well I remember when my buddy moved from detroit to seattle in late 80s. He told me how they had no income tax and how his license plates cost him $1200. mine in michigan, were we had a 4% sales tax, 4% income tax and my plates were $28 a year. Back then i earned about $20k a year, so my total state tax burden was about $1000, plus i got a renters credit that reduced them more. He had no job, was struggling to get a position in field and earned a few thousand. Sales tax and state fees, take advantage of the poorest in society, while income tax (especially a progressive like some states have) goes after the wealthiest.
So, you’re right, they’ll cut the sales tax then they’ll either cut the budget, or more likely raise/create other taxes to make up for it. Either way people won’t like the results. It’s shown in a repeated numbers of polls/studies, that people think they pay too much taxes and get too few services, whether tax and service levels are going up or down.