There are some websites that are both super aggressive about timing out your session and also make you play hide and seek for the login button. Of the sites I use frequently UPS used to be about the worst offender but the most recent version of their site does have a usable login link.
Vanguard is another one that drives me up the wall. Going to Vanguard.com doesn't have a sign in area to autofill with a password manager; you have to go to the personal investors page. And sessions are hard limited to 15 minutes so you have to jump through these hoops every time. I have the correct page bookmarked but even on that page the log in boxes don't appear until half way down.
Even the solution in the article seems to suggest using cookies.
I don’t understand the problem, if people want to try or sign-up for your service they’ll locate the signup button. That’s a one time problem. A hidden login button just annoys existing customers.
My feeling is that this is down to testing without privacy in mind. Your site might be fine, but others aren’t so a minority of users will clear cookies at the end of each browser session. That’s not a senario most will test for or experience.