Such a tortured life US-20 has had west of Elgin over the years. So many routings, so many ROW's.
My take is that with the recent outburst of growth in Hampshire, Huntley and Plato Township, it would be a huge mistake to terminate the Elgin Bypass Freeway at a new Randall Road traffic signal (of any kind).
While Larkin Avenue no longer supports the same type of traffic types it did when the intersection with the Bypass was conceived, I think it should be reduced in priority relative to the bypass to favor Randall Road.
The only concern is actually on the west side of Randall Road since that is a completely different school district.

The "center of gravity" for traffic as these new subdivisions get built is going to shift west to IL-47.
So I would stub Larkin at a new Randall, and put your money into improving the flow of Randall with US-20.
The only objectors I can see are west side commuters who prefer to drive into downtown Elgin to pick up their Metra ride. Stubbing Larkin and forcing them to circulate via Randall would probably make them grab their ride at National Street via IL-31.
Fortunately PACE does not run any buses external to Larkin from the west, so nothing to impact there.

Finally, ambulance access to St Joseph's Hospital on West Larkin could be impacted.
Emergency patients would be re-routed to Advocate General Sherman @ Randall/I-90 or have to go west to Northwestern-Kishwaukee in Sycamore.
I would bet $10 if Larkin gets stubbed at Randall a new hospital gets built on US-20 in Hampshire in 3 years.