Where are you going to put the laser, that pushes the laser, that pushes the spacecraft? And what's going to keep that laser in one place?Well sure there's a point in it -- it makes restocking the propellant unnecessary. Higher up-front costs, lower ongoing costs. Both solutions are feasible, and if you know enough that you can calculate that economic tradeoff hundreds of years in advance of the technology being ready, hey man, will you be my investment advisor?I'm not arguing against an interstellar spacecraft with a light sail being pushed by a laser; that makes perfect sense. But there is no point in having a light sail on the laser. It stays in the solar system, and it can either carry fuel / propellant or be restocked if necessary. Or replaced: I would imagine multiple lasers would be better than one anyway, for redundancy purposes.
It's not really an economic tradeoff, but physical one. It's less efficient to keep a laser in place with another laser, than it would be to... say, just have two lasers on the same platform pointing to opposite directions. Which itself would be kind of silly if you have access to better sources of propulsion.
Too many lasers! Unless there is a nuclear war in the future and cats develop the ability to shoot lasers out of their mouths.
I think you misunderstand the situation. Nobody is proposing a laser to keep the laser in place.
Note that at one point we are talking about laser-pumped lightsails and another we are simply talking about lightsails. The distinction matters!
The station-keeping lightsails are conventional lightsails using the sun. They hold the laser in place that is firing into deep space to accelerate the starship that is too far out to get meaningful propulsion from the sun. I think a gravitational tether to Mercury would probably be a better option at least at first--but if you have enough starships you'll need to have separate facilities and there's nothing else down there to anchor them to, it will have to be lightsails.