But also, we don't have the technology to do that, either.
The amounts of energy can be as little as you want if you go far from the sun where orbits are very slow and very little energy needs to be used to move an asteroid in any direction you want.
The only thing you need to do is to be patient. A lot depends on how greedy you are, if you want a smaller one it gets exponentially easier.
Just read this 10 year old report: https://space.nss.org/technologies-for-asteroid-capture-into...
"Reasonable" is subjective to define, but there are many multi-decade projects running right now so I don't think of multi-decade projects as unreasonable.
Things like sending man to the Moon or building Space Station would have been deemed "pure sci-fi" with the approach of the parent commenter.
All the things above are fully realizable in the coming decades, they are not in the realm of science fiction what so ever they are merely engineering problems.
2. Define “technology”
The meta-technology of R&D and socio-economic programs that will make these things happen exists and gets better every day. If a method to perform the needful does not exist, it will given the right conditions.
On earth, the nuclear reactors are radioactive rods that heats up water, to create steam, to spin a turbine, to create electricity. This is like a 5 stage process to indirectly generate electricity. But all the intermediary products are now radioactive.
So in space, I assume you can use the same steps to generate electricity, and then use the electricity to run a furnace, to heat up the minerals to melt it into pure metals.
Or is there some other process of using the nuclear radiation directly in space?
But really, reactors are extremely simple. For example, on Voyager missions the it is just a hunk of metal that is constantly hot.
https://en.wikipedia.org/wiki/MHW-RTG
You then do with that energy whatever you want.
You can use part of it to power electronics and actuators, part to melt a piece of asteroid and part of it to convert it to ions and send whichever way you want.
Also, RTGs have been used on earth, contrary to your implication they are only in space for safety reasons. Russian equipment in the arctic, for instance, has been powered by RTGs.
The point is you don't need huge complicated nuclear reactor to produce practically endless supply of energy in space, which is what the parent said he thought is a problem.
You probably need more energy than RTG but probably not as much as most people think. If you can apply a steady force for years, you would be able to give the required 10-100cm/s velocity delta to even large asteroid.
There are and have been fission reactors in space already. RTGs seem to typically be in the hundreds of watts, while the reactors are more in the kilowatt range.
The reactors are not RTGs, and they are definitely a lot more complex.