Your hairdressers really aren't trying to rip you off when they tell you salon colours are better than box dyes. They genuinely believe it because it is what they are taught.
Hairdressing courses are delivered by colour houses. I train at a Wella Center of Ellexcence. We are taught that Wella is the bees knees and everything else pales in comparison. The salon I help out in on a Saturday morning, the boss was trained by L'Oreal. They use L'oreal products because nothing else compares.
If you look at advanced colouring courses, which hairdressers take after graduating college, they are delivered by colour houses www.capitalhairandbeauty.co.uk/training/cutting-colour-courses
I'm on an adult learners course, so as soon as we were taught that box dye is the Devil's work, our immediate response was "Why?" The tutor, also taught by a colour house, could only reply that the developer was different, box dyes use a stronger developer than is necessary for most hair types. It wouldn't cover grey if it didn't.
Hairdressers then see hordes of people with a build-up of dull, flat box dyes which cements their notion of box dyes being the Devil's work but this isn't the fault of the product, it's the application. When I used to use box dye, like another poster and many, many other people, I'd just slap it all over my hair regardless of whether it was just my roots that needed doing. It builds up leaving the colour dull and flat but a salon brand would do the same if it was applied that way.
There is a skill to colour that a home colourist won't have been taught eg understanding the different levels and tones and how they interact with the base colour and which developers are best for which hair type, so the results from a salon should be better but this is skill not product. If you are darker and/or stick within the same level, there is no reason (other than application) why a box dye won't look as good as a salon colour.
Although, Wella's quasi colour is super, super glossy. I've never had the same shine from a box colour. It might have just been the shade and the client's hair but I'd kill for shine like that. I don't get it from the perm colour I use (also Wella).
It's the same with Henna. We are taught to always take a test cutting and check for metallic salts if someone has used Henna because Henna has metallic salts in. I questioned this myself because as a young, dumb teen when I was asked if I had Henna on I lied my ass off and my hair didn't burn off when I permed my henna'd hair. Plus, how does a plant contain metal? It made no sense, so I researched it myself and learned that most henna colours have metallic salts in them but the all natural ones (such as Lush) don't. Saying that, if you are asked if you have Henna on, don't lie. Let the salon take a test cutting and do their thing. A chemical reaction with metallic salts is pretty violent and not something you want happening while your hair is attached to your scalp. It literally smokes and fizzes.