It's a little more complicated than you assume. The cost of doing business varies widely by country. Not just the sales tax or VAT that gets passed to the consumer, but the corporate income taxes and other fees paid to governments. And with some governments there are a lot of other fees. For example, the company I used to work for was required by an un-named European country to pay for an annual "audit" by the government regluatory agencies. Said audit cost $250K, and involved some government people showing up and drinking coffee for a week.
I don't know of any state in the US that charges sales tax on subscription services, but I suspect that some other countries do. And in those cases, the $250K auditors might look for customers who reside in the country, but pay for their subscription via the US. If you were managing the company, would you risk fines and other penalities by NOT requiring customers who relocate to the country to become part of that country's customer base? So, it's not Adobe trying to protect itself from customer fraud, it's the government.
Adobe could, of course, be wholly egalitarian and charge the same price to everyone in the world, regardless of the country. And in doing so, eat the increased costs of doing business in some countries. But they obviously do not. In end, Adobe sets prices using the same old formula that companies have used forever.
Price = Cost+(X+Y+Z) where X = Supply, Y = Demand, Z = Whatever the market will bear.