People would find ways to hide income from their governments, to avoid paying tax on it; people would stop saving enough of their own money for retirement or other reasons, to avoid paying taxes on that money (which was likely taxed when it was first earned, or if not, may be taxed again when spent, depending on the type of account it is saved in). Most people would buy less, not spend more if they have fewer dollars in their pockets after their income is taxed more. So would governments. Infrastructure would suffer. People might buy more things which are harmful to their health, or to the health of the economy or ecology and might cost the government more in health care spending or to correct those problems.
The ideal would be to increase income for the government, while not hurting individuals too much. For example, I live in a state in the US which has a state sales tax, and in the US we are taxed on interest income and also wages, income and earnings, plus income earned outside the US, too. We pay annual or monthly property tax rates based on the zip (post) code we live in and the assessed value of our property.
If we got rid of the consumption tax, we would likely experience increases in all other taxes. For example: A huge part of our tax structure is gasoline taxes. Our public transport systems in most places is poor; that gas tax is paid by hundreds of millions of people on the road nationwide. If you get rid of it, and that tax amount is about 40% of the cost of a gallon of gas here,  people will buy more gas. Sure.
But they will also pollute more, rip up roads more, cause more traffic accidents and create massive roadblocks. And, the schools they send their kids to will suffer. The incentive to find alternative fuels or more eco friendly options will disappear as we guzzle it all until it's gone. The property tax we pay where we live pays only so much to local schools; it will go up too.
Gas taxes are distributed to so many places, their loss will reverberate for a long time. You'd have to make the income taxes so high most people would do anything not to work, not to work on the books officially, or will work so hard to hide the income, the government will waste time, effort and money hunting it down. Penalties for non payment would increase. Jails would be filled, clogging the court system.
People might agitate for better public transport, but might not get it and not in time to alleviate the problems. They might agitate to get better schools but there wont be the money to improve them. They might agitate violently for tax repeal. They might move to another state for better schools, or to another country to work, destabilizing their neighborhoods and cities, or maybe invest in other countries, not here. Living and working elsewhere, US citizens still have to pay tax on what they make outside the US, but they are usually paid more or given tax free benefits to offset that when moving away. Immigrants which staff our hospitals and teach in our schools, or who come here to study in college or start businesses here, might stop doing that. More Americans will emigrate out of the country or become expats, trying to find better options.
Unintended consequences will occur.  They always do. Tax avoidance in real life always creates a situation where on paper a trade off would work, but because of human nature and the desire to pay as few taxes as possible; it usually doesn't. Consumption taxes allied with income taxes and closing loopholes so people limit the taxes they pay but don't eliminate them or pay nothing, are probably best for striking a balance, and are the most efficient & fairest way to collect needed taxes to run governments, and provide the most for the most people.
