That used to be the case, but not so much anymore. 888 and 877 have been used enough by major companies over the past twenty years that most consumers know they are TF. The companies who claim 800 is the only way to go and not 888/877/866 have a vested financial interest in convincing you of that.
(Note: 855/844/833 have much less awareness, so my omission of them above was intentional)
Also, not disputing they are really valuable, I know that’s true from personal experience as well.
I’m more arguing that 800 numbers are valuable for a similar reason to diamonds being valuable. It’s not because diamonds are super rare or truly needed, it’s because the marketing has been so effective on them. The unbiased studies I’ve read show 888/877 are just as readily known and give a similar positive brand image as 800 numbers are. The industry doesn’t want to admit it though because they’ll lose out on the hype money.
If you're setting up the inbound call center call routing for something like selling slapchops or asbestos-related personal injury lawyers (just as an example of television direct marketing), a vastly higher percentage of the age 55+ target market recognizes 800 immediately but is less certain about 888, 877 and others.