For one, in many cases the XML + XSLT is more compact than the rendered output, so there are hosting and bandwidth benefits, especially if you're transforming a lot of XML files with the same XSLT.
Because those neglecting it are the same that want to remove it. So it's not “we want to remove it because it's neglected”, but “we want to remove it so we'll neglect it”. This is a pretty standard M.O. for the destruction of the commons.
If you look at the WHATWG GH issue, you'll see that two distinct, modern, maintained implementations of XSLT, one of which in Rust (so considerably less likely to be affected by memory bugs) have been proposed as alternatives to what's currently used in WebKit and Blink. The suggestions has been ignored without a motivation, because the neglect is the point.
Most of the issues of using client-side XSLT is that browsers haven't updated their implementations since v1 nor their tooling to improve debugging. Both of these issues are resolved improving the implementations and tooling, as pointed out by several commenters on the GH issue.