First, ICBMs are indeed faster than the hypersonic weapons currently in development, but it seems you are dramatically overestimating their maneuverability. They have some, sure, but they still follow a more or less ballistic trajectory. They aren't really easy to intercept, but they are easy to track and model, which makes the job somewhat easier. It's doable, if not a 100% success rate.
The bigger issue with the above as it relates to weapon systems currently in development is that you assume that forthcoming hypersonic weapons are using the same booster for the same mission as other weapon systems currently in the arsenal, specifically ICBMs, which is not accurate. At least here in the US, there are no plans to arm hypersonic weapons with nuclear warheads or to employ them in strategic roles. All of the systems currently in development and foreseen for the future are intended to serve a conventional tactical or theater role, performing long-range stand-off strikes in airspace that is denied to our current forces (e.g. by sophisticated air defenses or by shore-based anti-ship missiles that keep carriers out of striking distance).
Furhter, if they did come in nuclear variants, there would be no way to safely use the conventional variants for fear of an adversary mistaking it for a nuclear launch. There is then a likelihood that they would launch their own nuclear counterattack, and obviously no one wants that. The Pentagon has stated that their goal is to have thousands of these available for conventional use, so arming them with nukes would be counter-productive.
I don't know a ton about the SLRC (1000 mile cannon), but based on what I have seen, there doesn't seem to be a lot of room for concern just yet. It's largely on hold for the moment while the National Academies Study it and create a feasibility report, so to me it sounds like they know it's a big risk and are getting outside opinions. Based on what's public, it seems that it would use some combination of traditional artillery shell explosive propulsion to get it going followed by a rocket booster. My major question is why would this need to be a gun instead of just using a missile, especially since the Army is working on fielding its own ground-based hypersonic missiles.
Either way, if you don't dream big, you don't make big technological leaps. The key is to dream big but pull the plug if it becomes obvious that the program is not feasible. DoD is not always the best at doing the latter part of that on time.
This is not an accurate statement.
Do we know that the majority of its range comes from a shell propulsion system? I haven't seen that but that would definitely be eye-raising if true.