I don't think AEB should ever be a deal breaker for a first step into entry level DSLR.
A proper deal breaker would be not having access to manual exposure settings, or not being able to turn automation features off (not uncommon with consumer point-and-shoot cameras). Automation features invariably slow your camera down. If you are taking pictures of events and kids, it is more important to 'capture the moment' - the moment that the kid's eyes light up, or a group of guests laugh at a joke.
To do that you want look at 'shutter lag' and keep it as short as possible. Here is a review of the D3400 concentrating on shutter lag - and those timings look reasonable to good.
Many people use AEB to compensate for not being able to choose the right exposure.
But it is better to learn how to use exposure lock and spot metering modes to get the exposure right, rather than to use AEB to get at least one shot quite close.
That said, where exposure bracketing does shine, is in landscape photography when using a tripod and AEB to substitute for a graduated neutral density filter. You can use manual exposure settings combined with AEB to get a set of exposures that are just right for the sky and the foreground. Later in editing, you can blend between the exposures to get the final picture.
You can do this by just changing the exposure manually, but AEB allows you to avoid touching the camera and moving the camera slightly between exposures, which is much better.