They can, but don't get credit for it in Google's page rank. Which to me makes the whole complaint sound dishonest. They want to have their cake and eat it too.
Buy a 5$/month Protonmail account and forward your gmail to it, and slowly migrate all of your various email-authenticated services to point to your protonmail account. Plus Protonmail makes it very easy to run email from a domain that you already own, like your portfolio domain.
I pay for Fastmail and I don't even use them (waiting for multi label support) just to ensure they remain an option when they support the feature I need to move away from Google.
Switching from labels to folders has been painful as part of the FastMail transition, but I'm largely glad I made the change. Now my mail is standards-compliant and I don't have to deal with all sorts of crud when I have third party mail clients that don't support Gmail's custom stuff.
I know FastMail is working on JMAP, which ideally will be a new standard that supports labels, but if it takes off, it'll be a number of years before labels is something you can assume a given mail client will support. I use platforms that rarely have official app support (aka, not iOS or Android), so wide standards compliance is a big key.
For everything else (docs, hangouts, calendar etc.) simply host your own nextcloud. You can also go one step further and run a searx instance and you wont even have to rely on Google search (well, still kind of) anymore.
You can also host your own inbound mail, and use gmail for sending. You can add your personal domain email as a "send mail as" entry on gmail, and configure your personal email to use Google's smtp servers. That way you avoid issues with your domain's IP not being trusted by other mail servers.