I don't think it's meant to imply that it cannot be used with cold water instead. "Hot water only" just means there's one supply, which happens to be from the hot water heating tank it's paired with.

Call Franke and ask.

It does seem strange that Franke doesn't have little dispenser taps for filtered tap water. I think they used to sell a water filter (or they still do), so they must have taps for this.

I agree that a tap labeled as "hot water only" can pass lower temperature water too. My guess is that the marketing people are out of control.

I'm eager to know what the differences are between all the Franke models that look the same.
3100 4100 1030 and 1100

Here are some that have two handles (you get either hot or cold, from the same spout).
LB22
LB32
LB42

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Are you aware of the advantages of IHW?

Spoke with Franke tech support. It should work fine with cold water. Part of what makes it designated a hot faucets is that the fill lever is spring loaded so it shuts off when you release it. Franke point of use cold faucets have standard valves.

There are also regulations for cold point of use faucets sold into California in Vermont requiring no leads designs. They thought those regulations may be going nationwide in a couple of years.