What's reasonable? Well, from what I can see, whatever is convenient for those in power. What's the public interest? Why, whatever the government says it is. You see, it all depends on what the maaning of 'is' is.
They'll torture and manipulate those words until they get just what they want which of course is to take any dissenter and send him to a parking lot surrounded in chain link fence and a battalloin of riot police a mile away from anywhere meaningful.
Among the ideals of the very founding of this nation is that government will never suppress dissent or unpopular ideas. Now those in power spit on the sacrifices of those who gave it all for our freedom. For what? So they won't have a bad photo op of protesters as some high and mighty official rides by.
Such behavior is disgusting and contemptible. Such raw, soaring arrogance is what I expect from the King the founders rid us of.
This is a good issue for the courts because they will be very deferential to such an important public interest as protecting the President, but they will have a broader view than the Secret Service.
The tricky issue is not safety but order- and under the First amendment the courts will allow only minimal restrictions on that count ( which these Clinton-era restrictions overstep IMHO).
It's a great example of the First Amendment in action in the real world, just the kind of issue it was made for.