And this is how really terrible time situations occur.
Personally, I had servers configured with google and some other semi-public servers during the last leap second, and (traditional) ntpd did lots of weird stuff, so I ended up with pretty mushy time that day.
It's hard to get reliable upstream NTP servers--it was easier to point to Google. Google smeared, so my servers smeared, so all my downstream clients smeared.
I don't know how much my servers currently handle, but at one point they carried 1% of the North American pool NTP traffic.
Since it's not identified as an alternate time scheme on the wire, there's no way for downstream ntpds to know and refuse ut1. Falseticker checks help, but don't eliminate the possibility of following the wrong clock.
It'd probably break something but I can't for the life of me figure out what.
UT1 is an evolution of solar time, and wobbles when Earth does because it's using the Earth and Sun (and other bodies) as a clock.
UTC is TAI with leap seconds added when UT1 drifts too far away.
EDIT: Most computers end up using a modified version of UTC where the leap second is smeared at the NTP level instead of explicitly experienced. So any computer that uses that could probably use UT1. But we couldn't use UT1 universally.
One of the key reasons for moving away from UT1 or UT2 as the standard broadcast timescales up to 1972 was that the time broadcasts were (and are still) also frequency broadcasts, so when they adjusted the length of the second to match the earth, they also had to retune their high-power transmitter so that the advertised number of cycles per second was correct. And when this retuning happened they also had to promulgate the new adjustment factor to all their users who needed actual SI or ephemeris time seconds instead of rubber UT1 seconds.
See this page: https://www.ucolick.org/~sla/leapsecs/dutc.html
And scroll down to "Implementing the plan outlined at Torino", taking note of the "Notable event" column.
Edit: I think I misunderstood your question. This table shows the results of what would happen if we just stopped adding leap seconds.