The clear solution to this problem would be to move over to a territoriality-based tax system in which all taxes are levied depending on the tax rates prevailing in the country where the business is taking place. This would simplify the tax code; remove absurd barriers to capital returning home; and generally move to a globally harmonized system of corporate taxation.
A one-off exemption is a second-best attempt to deal with this problem. This poses a number of different problems -- in particular, businesses come to see these one-off exemptions as inevitable, and so stop repatriating profits in all other periods. This ends up "heightening the contradictions" in the corporate tax system, as it were, and ensures that exemptions become regularized.
The other chief complaint is that repatriated corporate profits don't go to productive purposes. This is the claim from Howard Gleckman at the Tax Policy center, who draws on research in the field. The paper he references finds that repatriated profits were largely dispersed to shareholders.
Here's the thing though -- those shareholders then went and did something with that money. Perhaps they reinvested in company shares; maybe they went and bought a yacht. In the case of your left-wing Keynesianism, you issue a bond for a dollar and then spend that dollar on some sector of the economy. That may not logically preclude an economic expansion, but you can see what the difficulty is. But in the case of this right-wing Keynesian policy; you do have a genuine influx of foreign cash into the economy. Perhaps corporations aren't the ones spending the money. But someone sure gets that money and spends it. To be sure, there is a parallel problem that a large enough capital influx will adjust exchange rates however.
In general; I'm increasingly skeptical of tests like the one in the paper I mentioned, where you have a specific experiment applied to some subgroup of the population and you try to learn about the response. Even if you get the identification right (and that paper spends a lot of time arguing that they have some); it's just difficult to extrapolate from there to think about what that might mean for an economy as a whole.
That makes me think this right-wing Keynesianism may be underrated. Moving to a better tax system is a win; and shifting cash domestically in the short-run may be a win too.