This is a UX problem, not a technical issue. I think you may be misguided in assuming that if the "www." portion was present to users that they would automatically understand the issue at hand.

This is a false assumption. Your average user has probably never realized that "www." is not optional, and that with and without it are resolving differently.

This is very much a problem that you can, and should, solve FOR your users via properly configured DNS settings. Otherwise you're picking an odd hill to die on.

I promise I mean no disrespect. In fact, to put it another way, even if Chrome did what you said, it would not solve your issue - which is users failing to reach your site. Hope you can get it sorted with your provided, or switch to another. I've had good luck with Route53 via AWS.