BA is seen by many as some kind of glorified secretary, and testing is like mum checking the work.
This is it - they're missing the point. A good BA is worth their weight in gold - they'll have done the work to figure out exactly what needs to be done, what needs to be thought about, what's affected by any project or change - the architects if you were building a house I'd say.
The dev implements that (and if the dev needs to think beyond dev, that's because your BAs aren't doing a good job). The builders - they have expertise, but their main job is using that expertise to follow the BA's plans
The tester doesn't (well, shouldn't) care about the dev, they make sure what the BA specified, happens. They are both diligent, and creative (my DP started out a tester, he is absolutely devilish in his ability to think of things the BA and Dev missed). They are the safety inspectors, the customer, the ones making sure they've got what they expected.
Unfortunately, in a lot of companies, the BAs just write down what the business says, without thinking it through, the developers develop what they want will only minor reference to common sense or what is specified, and the testers stick to the rule of what's written in front of them without thinking about any side effects, alternative routes, or what's best for the business. We could all do better.