Having followed the mixed-breed dog stats in the U.S. for a few years now – and having been a lifelong believer that a mix is a fine dog, and a shelter or other source of mixes is a great spot to find one – I no longer think so.
Currently, the majority of mixed breeds in the U.S. are likely to have a 30%+ (even +++) percentage of pit. And pit + staffie, and other guard-type dogs. High prey drive dogs. There is nothing inherently wrong with that, pits and pit mixes can make great pets. But if you know that’s not what you want, it will be hard to find a dog from a shelter or other random source that doesn’t have that DNA enough to matter.
Aussie and BC are also widely prevalent. Both breeds have spread widely in areas allowing indiscriminate breeding. GSD’s, huskies, and other high drive breeds have become more widely found in the mixed breed populations, likely due to BYB.
Also, just because a randomly-sourced dog is a mix of well-made, good-minded breeds does not mean that this one will be. A lot of low-quality breeding is going on, in huge numbers.
Also, you cannot tell what is in a mixed breed dog by looking. No one can, no matter how much of an expert they consider themselves to be. Generally speaking, genetic traits can hide. Traits with particular genetics can alter other traits. For reasons of genetics, mixed dogs can look nothing like some of their large % contributors.
Mixed breed dogs today are nothing like they were decades ago. The good natured mixes of beagle, spaniel, terrier, etc., from decent purebred stock, are vanishingly scarce these days. There is no way to tell those that do exist from the randoms with all of the undesirables on board.
For that reason my next dog will probably be my first ever purebred. That won’t guarantee anything, of course. But it will mean that it won’t be carrying something I’ve already decided that I don’t want in my next dog.
Otherwise bringing a mixed breed into the home is like any other inclusion of any animal whose background isn’t fully known – you get what you get. 