From what I know once the amphitheater is ready they will use it after the races to try to stagger those leaving once the race ends. So everyone isn't trying to leave all at once. But it won't be ready for this years race.
Additionally I can think of many reasons why they would want to put on a big show downtown this year, but obviously not being able to use their amphitheater is the main reason. If as I understand that it isn't going to be ready in time is accurate.
For one, a large part of the Austin population hates COTA. The fact it is a professional sport to start with, and a race on top of that is enough to make it really hard for them in a town like Austin where most of us are ignorant of car racing and just associate the sport with NASCAR and conservative toothless rednecks. On top of that how they went about getting and planning to use tax money from the state and the whole mess with that really alienated many people. Justly or not, they got a lot of bad press. So they need to engage the population of Austin. Sponsoring the Fashion Week is a fantastic start. Putting on a large Fan Fest downtown would have been another. But they sure do have their work cut out for them and a very hard uphill battle to win over Austin. For COTA to be successful it will need to win Austin. The worst thing they could possibly do is take Reid Ryan up on his offer to use the Dell Diamond in Round Rock.
Another big reason I can think of for having a show downtown is there is a reason they chose to locate the race in Austin. It has a kick ass party scene and is a hell of a fun town. They want those that attend the race to have a good time, and getting them to hit a show downtown after the race and likely hit the town after the show would be big in getting those that come to town for the race to really enjoy their trip and tell their friends what a great time they had and come back again for next years race.
And another reason is they need people to spend money in Austin. The $25 million they want from the state depends on Austin signing off on it, and for Austin to do that then Austin needs to make back all the money it spends on overtime and everything else with tax revenue. If the economic impact of the race and the tax revenue that Austin brings in, isn't enough then they will not get Austin to sign off, and possibly not get the money from the state. So that is a big reason to insure more people spend money downtown that week.
Lastly they could have just hired C3 to put on a big show on Auditorium Shores very easy. C3 has so much experience doing shows there that C3 could have done it blindfolded with one hand tied behind its back, no sweat. lol. If the Waller Creek project was not currently under construction then Waterloo Park would be a great other option, but it is u/c so it isn't an option.
As for the other places downtown. For the Erwin Center that is basketball season. They can set it up pretty quickly but UT will want a ton of money if they are going to go through the trouble. They would demand a LOT more money that I would think COTA would ever think of spending. Putting on a show at the Erwin Center is expensive as hell. Both for UT to host the event, and for whoever is putting on the event. It is a major venue, and not cheep or easy to use. For Zilker it is a bit far but a good option if it is available and all the days aren't used up already.
My advice is to go the SXSW route and sponsor a bunch of parties all over town. During South by there are over 900 shows a day seen by almost a half a million people a day (
Note: many of that 500,000 are the same people seeing multiple shows) Sponsor some big acts at the larger venues like Moody, Stubbs and Mohawk. And sponsor lots of smaller parties and acts all around town. To do that though takes a lot of work and planning way far in advance, but there are plenty in Austin who can get a big time party together pretty quickly and do a much smaller scale version of South By. Another option get permits to shut down 6th and Congress and put on a street fest. Something like what the ROT Rally does on 6th and Congress and what Bat Fest does on the Congress Bridge. Just shut down the streets starting at 7pm and put up a stage right in the middle of the intersection. Most of those streets close down every weekend anyway, and with the F1 Grand Prix going on, and many more in town than usual there will already likely be more street closures downtown than on normal weekends. So just get a permit for a stage or two and rock on.