Yes and no. GMail does support IMAP access (Go here to enable it: https://mail.google.com/mail/u/0/#settings/fwdandpop). IMAP is a standard that allows you to access an inbox remotely.
OTOH, as long as you are using @gmail.com in your address, you are at their mercy. Go to https://www.gandi.net and purchase a domain name, it'll cost you <$10/year and you will own it. Make it nice and professional (yourlastname.net for example). [email protected] is the sort of email address you'll own your entire life.
FastMail is a paid alternative to gmail which people consistently recommend here. I am happy with GSuite personally as I really like the GMail interface, but you can look here if you want an alternative: https://www.fastmail.com/ (~$5/month plan for custom domain)
GSuite is the paid version of Google's services (~$5/month); as you said, it is perfectly fine for Google to charge for services. And as it happens, you can use your own domain on GSuite, so you could use your new email there. https://gsuite.google.com/together/
PS: If anyone is having trouble and needs help setting this up, shoot me an email (profile).
I don't really want to move to some other service - what I want is the assurance that Google is not going to do something funny with my account or service and unfortunately if they do I will have no recourse.
When I got my Gmail account in 2004 Google was this amazing website that will give away free services and their motto was "Don't Be Evil", at least that was my impression. I still like most of their services, just don't like the "free" deals anymore.
I've been switched for over a year now, and I check Gmail once every couple weeks now, instead of daily, like I did when I first switched. (I also have a Gmail vacation responder set up to automatically email literally anyone who emails it to tell them I don't check it often and what my new address is.) Yes, I'll probably keep the address forever, but it certainly isn't used much anymore.
Ironically, I had issues with my Gmail address long before I wanted to change providers: My main Google account address has my old last name, and Google's archaic infrastructure[1] for identity provides no way to change it. I had a newer Gmail address forwarding mail to it, because I didn't have a way to move all of my purchases like Android apps and the like, over to my new address' account.
[1]Microsoft has no issue with your account having multiple Microsoft-owned and/or third party email addresses and letting you change the primary one. There's some wonkiness with different services not recognizing your primary email has changed, but largely speaking, this is manageable. I have the same Microsoft account as I had years ago, everything carried over, but now identified by my current email address.
Zoho's webmail is currently much better than RunBox but the latter is undergoing a beta test of a new modern interface.
The only thing really bothering me is that you can't seem to set a default email app in iOS so mailto: links won't open the FastMail client. This is a super annoying client issue, but the service works incredibly well, no complaints here.
N.B. I have no affiliation with FastMail or Gandi whatsoever, just a very happy customer.
What I did was to sign up for Fastmail with my own custom domain and forward stuff to my @gmail.com address. This way I continue using Gmail but with my own domain.
I could do this with GSuite (and in fact I did for a couple of years) but GSuite accounts often have limitations compared to regular Gmail accounts and I didn't want to deal with that.
Google has been a lot better about this lately, but it still happens.
Yes, forward them to your new email, preferably using your own domain name. Start giving out your new email to people, reply to your gmail email from your new email. It takes time but after a few years you can ditch the gmail completely.
I'm quite a bit uneasy with Google lately but it's not feasible for me to move to another e-mail provider because my user account on many other websites is tied to my Gmail account and not all websites support e-mail changing.
At this point, I would argue that Gmail reached a public infrastructure status and it's not acceptable of Google to take actions without public consent.
It is perfectly acceptable if Google decides to charge for de services as it will happen with any public infrastructure that has running costs but it's not acceptable for Google to force people into situations or engineer their behavior just because provides the service free of charge.
For example, in my country, the electricity is generated by private for-profit corporations. However it would not be acceptable if these corporations start changing the voltage of the frequency of the electricity and force people to use devices designed specifically for that electricity network.
I don't remember Google forcing me into using Gmail but I also don't remember anyone forcing Google to provide an e-mail service. They did a great job, it revolutionized e-mail but they did it to compete with Microsoft and Yahoo, thus for profit(back in the day everyone was using Hotmail or Yahoo).