As you say, it's
because the speech may later give way to force. It does go farther than American free speech law permits: the latter draws the line at something like "threats of immediate criminal action", whereas this would attack "propagating ideologies that one thinks will eventually lead the followers to criminal action". There are certainly deep problems with potential implementation here: e.g. the main American political parties would probably both accuse each other's ideology of eventually leading the followers to criminal action. One would want high standards for that (of, say, what percentage engage in what magnitude of criminal action; as well as evidentiary standards), and want it to be established in a mega-trial, or by a supermajority of Congress declaring war on an ideology; and even that might not be enough. I'm not necessarily in favor of Popper's approach, except in emergencies.
However, I think that, when most people use the word "intolerance" today, they include things like speaking racial slurs or expressing any negative emotion towards a demographic group. There are contexts in which these things are done, and manners in which they are done, in which, yes, they do give a significant signal that the speaker is the type who would cheerfully escalate to aggressive violence towards the targeted group; but also contexts and manners in which they do not give such a signal.
I think there is a distinction to be drawn here, between "always tracking whether this is likely to escalate to criminal action" and "just attacking anyone who vaguely resembles a known 'intolerant' group". The latter is essentially an autoimmune disorder, which has led to massive collateral damage and its own discrediting. The former ... has a danger of turning into the latter, certainly (which has an interestingly meta angle to it), but is there any version of it that is well-protected against that fate? I expect there's room for improvement compared to earlier versions. I don't know if it can be done well enough to be worthwhile.