Quite the contrary. The browsers people use are largely based upon open source engines. The cloud applications people used are built upon ecosystems of highly successful open source projects. Basically every major web development framework is open source.
The role of open source has shifted, but it's more important than ever.
That's why you start hearing FLOSS talking from governments: these days FLOSS does not means FLOSS but being able to grab free code to serve jails to end users... Proprietary development model is not sustainable anymore, and IT giants have found the way to sell mainframe-alike systems where the users just get dumb terminals, than they push FLOSS.
Today we not only need mandatory FLOSS in the public administration: we need a public IT development that push back the classic desktop model against the worst-than-classic-mainframes cloud model, starting forbidding certain web services for the public administration and reaching the point of forbidding modern web at a whole.
The role of open source has shifted, but it's more important than ever.