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Oh we absolutely could, we could have done it with 1960s technology in fact: https://en.m.wikipedia.org/wiki/Project_Orion_(nuclear_propu...

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The propulsion may have been theorized to get us up to speed, but there are many other factors, not least of which is shielding from objects while you're going a decent fraction of the speed of light. There's no obstacle avoidance routines with that much momentum.

At 1% of the speed of light, the energy of a proton is 47 keV. This is trivially easy to shield against. The energy of an electron is just 26 eV.

One would need to shield against galactic cosmic radiation, but this really isn't much more of a problem than shielding a vehicle in the solar system.

What about a micrometeoroid?

The risk with these if they are sufficiently large would be an explosion on impact. This is dealt with by placing a thin barrier in front of the vehicle. The particle explodes on impact with the barrier, cutting a small hole. The debris shoots forward, spreading, and is absorbed on a shield. At 0.01 c, a 1 microgram particle deposits 450 joules of energy. This is called a "Whipple Shield".

If necessary, parts of this system could be replaced during the journey.

I just want to be clear that this is all heavily theorized. The density of interstellar space has an assumed ablative rate based on speed of travel, but it wouldn't take much to exceed that. We are at least a few trial runs away from knowing, and that alone makes the prospect of interstellar travel far into the future. (again, repeating my main point)

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