They're not necessarily a bad idea, even though they'll have no impact at the destination. It's the journey
With a warp drive, people from Earth could routinely venture to the millenia ship and take tours of it, staring at the spooky frozen embryos or aging crew, still stuck in the world of 2100 like cavemen stuck on a raft going in circles in an eddy in the Pacific.
In inflation adjusted constant 2010 dollars, I'm thinking $350 for the flight out to the millenia ship and $50 for admission. The souvernier shop would make a killing and could easily be restocked from the warp ships. Of course the actual crew would quickly abandon the effort, so you'd have to pay college kids to dress up in crazy year-2100 costumes and speechify in the old way, but they work cheap. Since the journey is going to take thousands of years, the return on investment should be astronomical.
After the first thousand years of profitable business you'd even hire people to play tourists from earlier centuries, so new visitors could see what it was like to gawk at the "Twenty-One Hundreders" back in 2350.
Think of it this way, if you buy a ten year life insurance policy on your self, and within that ten years you don't die, would you feel that was wasted money?
If we launched that slow starship and humanity destroyed itself before building a faster ship, that would be a good investment as it would have saved the human race, humans would get to start all over again on a new planet.
If the starship was launched and humanity did not destroy itself and faster ships bypassed it on their way to the destination, then it is just like the life insurance policy you bought but never needed because you didn't die, that life insurance policy still cost you money however, would you feel cheated if you bought a life insurance policy on yourself and you didn't die, or are you paying just to ease your mind that your heirs and dependents will be taken care of in the event you did actually die?
A slow starship that eventually gets there is like paying money for life insurance it turned out was never needed, its purpose is to save humanity should the worst happen, and at least its development would be a step on the path to even faster starships.