Looking at what the PHB says about Backgrounds, it's easy to see that these features were intended to be used most of the time players wished to employ them. First, the PHB says that features provide concrete (ie, not abstract) benefits:
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Next, the language for features include things like "you may expect to" or "will support you" or "even across great distances". What's not said is "ask your DM", "at the DM's discretion", or "the DM may".
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Certainly, everything in the game is subject to the DM's discretion! But if something was intended to be a negotiation or requiring specific permission or rulings every time it was used, the books usually state as much, for example:
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Background features are presented in the same way a character's racial and class features are- abilities that you have, can rely on working when you need to as written, and not requiring much in the way DM oversight or discretion to be used.
Now as has been noted, if a Background feature isn't going to be useful, or requires negotiation with the DM to use, then that should be done in a Session Zero. Or, as the DMG says on page 26:
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Before the game even begins, the DM should know what the backgrounds of the characters are, and how to incorporate them into the game. The players should know what they can expect out of their backgrounds and features.
The reasons Backgrounds are changing is simply because this vital step was not being taken in enough campaigns that WotC was obviously not receiving positive feedback about features. What was meant to be a "cool thing" for players (and certainly not vestigial, as the text bears out) was simply not being that, for various reasons. So, the playtest seeks to fix this by replacing features with Feats- the idea being, the benefit of Feats will come up much more often, and hopefully without the DM having to make too many allowances for them in their worldbuilding.
What this does not mean is that backgrounds are becoming less of a tool for DM's- you can still do everything 2014 wants you to do with backgrounds if you want to- but enough people weren't doing this, again, for various reasons, that it's gone from a core aspect of the game to something optional.