Penalizing investment tends to push capital out of the US economy and into overseas economies, for one thing. Forcing US capital abroad is good for the rest of the world, but not for the US economy.
The problem with trying to attack capital is that it is mobile. This is like the whole Apple-and-Google-pay-no-taxes issue; there is a jurisdiction which allows them to avoid taxes so they sensibly move their capital there. You can try to tax it when it moves, but the movement just gets disguised as a business transaction. If you tax international trade (aka tariffs) you end up damaging the economy by impeding trade.
Barring international treaties which establish common taxation regimes worldwide, this will always be a problem for governments of wealthy countries trying to tax capital, because it is in the interest of less wealthy countries to offer very low tax rates in order to attract capital. Ireland has announced they're ending their practice of doing this, but someone else will offer it.
The brilliant thing about taxing consumption is twofold. First, consumption is tied to people while capital can live in all sorts of places and forms, and people have a physical location and a legal tie to a government. People are mobile, too, but less mobile than capital. People like to live primarily in their own culture, near their own family, business partners, etc., and even if they're willing to move to another country changing their nationality is a big deal, with all sorts of repercussions. And even if they're willing to do that, they're rarely willing to move to and become a citizen of a third-world dump of a country in order to get low taxes. Moving to France isn't going to reduce your tax bill.
Second, consumption is easy to identify. You can try to hide your consumption by having corporations purchase all of your homes, cars, toys, etc., and then let you "use" them, but the IRS already handles that sort of thing very effectively, even under an income tax regime. Use of such things is income. With a consumption tax approach it becomes even easier; you don't bother figuring out what percentage of that jet is used by which person and at what value to count it as income, you just tax the purchase of the jet. Doesn't matter if they try to work around that with lease agreements, or whatever, someone has to acquire ownership of the jet, and regardless of who that someone is, you tax them, which means the taxes are built into the lease, or whatever.
The remaining dodge here is for wealthy people to do all of their consumption overseas. I have my overseas shell corporation buy the jet in Barbados, where there are no consumption taxes, then allow me to use it. This puts us back in the position of having to figure out what portion of the jet's time is allocated to me and then having the US assess the relevant consumption tax to me, via random audits plus the threat of prison time if I fail to report and pay what I should. Same with foreign homes, etc.
But to the extent the wealthy can dodge consumption taxes with foreign consumption, it only works for foreign assets. Real estate, cars, caviar, etc., that are purchased in the US are easily taxed. Same with anything that is imported into the US. So unless the wealthy decide to spend most of their time overseas they'll do most of their consuming here.
I should mention that for many of the same reasons I think corporate income taxes are a bad idea. Corporations have lots of flexibility to relocate money to avoid taxes, and given the complexities of business it's non-trivial even to determine what the income is, and it's in that complexity where most of the loopholes live, and in any case, what's the point? All money ultimately belongs to people, even corporate money, and it has to leave the corporation before any person can use it. People are easier to tax, whether via income or consumption taxes. There's also the fact that corporate income taxes are effectively a hidden tax on customers (who pay more), employees (who make less) and shareholders (who make less), and I'm opposed to hidden taxes.