What's the big deal about multi time?

The short answer is "insurance wants it", especially if you're going to be flying multi-engine airplanes and doubly so if they're turboprops or jets. If you don't have it, you won't be insurable (at least not at astronomical cost) and you won't then have a professional flying job.

The long answer is yes, twins tend to be larger, heavier, faster, and more complicated than their SE counterparts. There have been thousands of pilots throughout history that simply could not handle a transition from a slower piston single to a faster turbine multi, and the more time you have flying larger/heavier/faster/more complicated twins the lower a risk you appear to be for a training failure to a potential employer.

Building multi time is a PITA because its 1. hard to do and 2. very expensive...but suck it up and find a way to get to 100 hours because, just like those "magical" numbers 500tt and 1000tt, 1000 multi will open doors for you down the road.

That said, a modern jet with tail-mounted engines is almost centerline thrust compared to the likes of piston twin with big engines on each wing (ala Baron or Navajo)...let alone something like a King Air.