Man, that would be amazing.
We actually have unlimited bandwidth, and storage isn't really a concern either. What does matter is the number of virtualhosts on each server. Each domain that we host increases the virtualhost count by 2 (one for http and one for https), and that's the main source of load for small sites like yours.
Each virtualhost increases the amount of memory that apache uses, and increases the downtime that we experience each time we restart apache. If we were to allow these virtualhosts to continue piling up from thousands and thousands of small, low traffic sites like yours it would eventually take several minutes of downtime to restart apache each time. A small downtime like 5-30 seconds is barely noticeable and most people just chalk it up to their internet being slow for a second, but if we have so many virtualhosts that each restart takes something ridiculous like 5 minutes people are definitely going to notice and complain.
Larger hosting companies get around the virtualhost issue by creating many smaller servers to distribute the virtualhosts over dozens or hundreds of apache installs. Since we use cpanel it is very expensive to set up each additional server because of licensing costs, but we can maximize the number of sites we host by cramming as many people as we can onto our existing 3 servers.
The monthly login requirement is in place, not to intentionally annoy people, but to keep our virtualhosts count as low as possible to keep our memory usage and restart time low.
Now, as far as keeping your account active, plenty of other people do it just fine for years. We have one lady that has maintained an active account using the same free HelioHost domain since 2007. She logs in once every month just like everyone else for 14 years and counting.
The guy that runs this independent monitoring site http://heliohost.grd.net.pl/monitor/ isn't a HelioHost admin, and isn't affiliated with us at all. His accounts that he uses to monitor our servers are identical to everyone else's and he has to log in every month to not just one, but three different accounts to keep them active. He's been running that server monitor since 2010. The only thing special about him is we have granted him permission to have more than one account at a time. There's dozens of other people who maintain active accounts for years on end too. Those are just two extreme examples.
When you don't log in for 28 days you will receive an email reminder to login to prevent your account from going inactive, and you have 2 days to check your email and login. If you save your password in your browser you can simply click the link in the email, which brings you to the login page, and then click submit on your saved username and password on the website. How long does it take to click twice? 5 seconds? That's all it takes to keep an account active.
Anyways, we get this request to not have to log in to cpanel all the time, and you seem like a person that would value equality. Maybe you think you're more important than everyone else, but based on your post it makes me think that equality is important to you. It wouldn't really be fair to everyone else to treat some people differently from everyone else. There's also the issue of if we make an exception for one person we'll probably have hundreds of other people come out of the woodwork asking for the same thing.
So, since we get this request all the time we have come up with two solutions:
You can donate instead of logging in. Each $5 you donate gets you +1000 MB storage up to a maximum of 5000 MB plus 1 month of inactivity immunity.
The new server that we're going to set up hopefully in a few months will allow you to never have to log in to cpanel as long as your $1 subscription remains active.
So option #1 probably doesn't appeal to you because you obviously don't need the storage space increase, and option #2 isn't available yet, but it might not appeal to you anyways since you want free. Anyways, I'm willing to give you a special option #3 that we haven't offered to anyone else yet. You can basically get the deal in option #2 early on Tommy instead of the new server. I don't want to do this for a lot of people because it would get confusing to keep track of everyone, but if you want to donate $1 for each month of inactivity immunity I'll grant it. So if you want to not have to login for the next year you can donate $12, etc. Eventually this deal will be offered to everyone on the new server so everyone is still being treated equally; you're just getting the deal earlier.