Not exactly new, we saw these but didn't have a label yet in 2008 election campaigns. The media, the "educated" extremists on both sides and the candidates themselves courtesy of their respective speech writers all use this tactic to sway more opinion and in some cases votes in their direction. Weasel Words, reminds me of the speeches of ancient Rome; just as invalid a practice then as it is now but to be expected.
Politicians have to weasel around. If they speak too plainly, they'll alienate their constituents. Voters tend to fixate on single, highly-emotional subjects, forgetting that an elected official has to deal with hundreds or thousands of issues, most of them mundane and boring. Elections are decided by hot-button topics of the moment, not by careful consideration of who will, over the long run, make the best decisions.
No, I do not believe that politicians should be allowed to use weasel words. This evasive and confusing use of language is so problematic, especially by politicians as they are civil servants: representing their electorate and have a duty to provide information and assistance to their people. Weasel words tangle that relationship causing distrust in the political system.
Weasel words should be allowed by politicians, but the public and press should call them out. A weasel word is an informal term for words and phrases that try to create the impression that something meaningful has been said, when, in actuality, only a vague claim has been communicated. While it is tempting to ban these statements, a more effective manner is to question the politicians who say such things.