I haven't seen it yet in person, so I can't really comment on how it fits in. Architects are often like music composers, they create things that the rest of us look at it and say "What the heck?". The idea was to try and create a grand transportation hub , not really as a memorial from what I can tell, but more about making a statement that terrorism wouldn't stop people from dreaming (or so I heard). I don't necessarily object to spending money on something like this, there are always things that need to be done, there are always problems, there are always threats and dangers, and if all we did was spend all our money and time on those, it would be a pretty drab world we live in. Whether I think this was worth it or not, it at least left something behind. People said the same thing about Grand Central, about the Empire State Building, about the original WTC, about the space program, how there were better, more practical ways to spend the money, but it left something behind, as did the original Penn Station (and think about this one, the old Penn Station was replaced for MSG and office buildings that 'would actually do things', knocking down Penn Station was sold as creating the modern NYC,it would bring efficiency to the street, be a 'hub of the economy' and the like....and in the end, was that an upgrade?
As far as why these things end up costing more than they estimated, there are a number of factors. I don't know if they granted an exemption for this particular build, but NY State has something called Wickes law, that when there is a public project, the state or city has to act as general contractor, rather than hiring a general contractor who brings in the sub contractors after submitting it for bidding. The idea was, in the depression years, to prevent a small group of contractors and subcontractors from getting all the work, this allowed the city or state to 'spread it around'...the problem there is that when you have a GC, they have all the risk on the project and also can keep the subs from screwing around, because if they do, they won't get jobs sent their way. So you have things like the electrical contractor telling the guy doing the plumbing "hey, do me a favor, when you go to put in those pipes, when you punch a hole through that wall, could you take out the conduit there?"........it lengthens the job. Plus unless things have changed, when you do private contracting, there is a finish date, and if the contractor misses that, penalties kick in (likewise, if they finish early, they get bonuses). As far as I know, that doesn't apply to public contracts, so there is no incentive to finish on time, and the longer it goes, more it costs.
It also is because state government often takes the lowest bids (by law usually), and often don't look at the firm's ability to do the job or their past track record. The city back in the 80's time and again hired this excavating and paving firm to redo major roadways, and every job this company fouled up, streets had the wrong grade, sidewalks, curbs would be left "hanging in space", sub surface elements like pipes and such broken, trees destroyed..but they were the low bidder. Same thing applies to materials, when they built the SF bay bridge, they decided to get the steel made in, no big surprise, China..and guess what, they ran into all kinds of problems with getting the steel delivered in a timely fashion, it was not unlike what we see with the trains we love, stuff doesn't ship on time. Train doesn't ship on time, we get angry, steel doesn't arrive on schedule and other things cannot be done, and that costs time which ends up costing money. Plus on government large scale jobs, you have inevitable change orders, someone decides they want this done this way instead of that, and that is costly as heck (contractors make a lot of their money on change orders). With public jobs, too, if the cost of materials goes up, the contractor can pass that along, on private jobs if the cost of materials goes up, the contractor eats it. That doesn't mean private work is a testimony to efficient production either, a lot of private projects end up taking longer and costing more than estimated, we just don't hear about it as much.
The other factor is that public projects often are done as public projects because no one else would touch them, because they involve big, messy projects that have a lot of risk with them. Putting up an office building or the like is a relatively finite kind of project, something like a public site like a transportation hub or a new subway tunnel or a bridge are infinitely more complex, on a larger scale, and it is why you don't see private firms doing those kinds of things, why you didn't see a private developer doing the transportation hub, for example, because there would be no profit in it for them, too complex. Infrastructure by its very nature is expensive, and doesn't offer much of a return, so it is left to public entitites to do it. The subway system in NYC is a good example of that, despite what some think, private ownership of the subway did not produce great service (or profits), it ended up leaving the subways a mess that took many decades to get out of. Even if the fare hadn't been fixed at a nickel, which was ridiculous, it is likely that private operators would have found in the end they lost money on them. If they charged a fare that allowed them a decent profit, they would not have the ridership to support it, and if they charged a fare to build ridership, it likely would cost them more to run it than they got in fares.