If inflation causes the nominal value of your hotel chain to increase 2%, you have to pay capital gains tax on this nominal gain (at least in countries where capital gains tax is not adjusted for inflation), leaving you with less real value afterwards.
Only if you sell. And if you're invested in a company that is only growing at the rate of inflation then I'd imagine they are paying a decent dividend which is very possibly a qualified dividend that has no tax associated with it. Reinvesting that into the company creates a compound effect far greater than the inflation rate and will be taxed at the LTCG rate one day when divested from.
That only matters if you realize the gains. If you own a business like a hotel, car wash, etc. and intend to keep it, you are not affected by value increases of the business itself. In fact, for many privately held businesses, it is not even known what the value of the business is because there is no reason to calculate it.
I'm not even sure how accurately some small businesses can be valued. A local cupcake lady or artist might run a business that makes decent money, but all the income and value is derived from their unique style. Remove them and the business is almost worthless.
If a tax on capital is instituted are there mechanisms to value such cases?
With the current wealth-tax proposals by Warren and Sanders. the owner first of all would probably owe zero wealth tax unless she was worth more than $32 million, or $50 million for Warren. I doubt any local cupcake businesses are worth anywhere close to that much.
Second, an actual business of that size would probably be owned by some other corporate entity created for that purpose, not an individual, and that entity would be paying its own taxes.
Finally, Warren and Sanders both plan on beefing up the IRS to answer these kinds of questions, which will certainly be thorny for some kinds of assets.