Are the problems with online purchases only outside the US?
AKAIK, 3D Secure is not used in the USA at all. I've only encountered it when attempting to make transactions with businesses whose billing/payment processors are based in Europe. For example, I was booking a live-aboard trip on a scuba diving boat in the Maldives. The company was actually based in Egypt, but their payment office was in London. They were using 3D Secure, rendering my US-based, major international bank credit cards useless.
People in the forum have reported running into 3D Secure issues when attempting to buy tickets for European railway systems, other Europe-based websites, unattended gas stations and highway toll systems. So it most often messes with you at automated kiosks or other non-staffed point of sales systems in Europe itself, or when trying to buy something (from anywhere in the world) at a website that uses a European payment processor.
I've never heard of 3D Secure interfering with the use of American credit cards elsewhere in the world (I've used my credit cards widely in Canada, Asia and Latin America, a bit in North Africa, and never had any issues). Maybe I've just been lucky but I don't think it's an issue for transactions that take place outside of Europe.