Robin Berjon points out how having Tweets embedded in websites is – like most "embeds" – a risk in terms of security (for the end users, mostly, but in theory also for a website itself), but also carries the risk of extracting meaning from articles should they really vanish into the void in the foreseeable future.
I've long advocated against embedding third party code into websites, but now there's a really good moment to finally pull the plug. Get those existing embeds converted into static content now!