> of course you'd need bigger parking lots than seating space
There is a tacit assumption in your statement. Of course you don't need vast parking lots around stadiums, and there are plenty of real-world sports arenas that don't have those (some examples [1][2][3]). The parking that there is is structural, and most people simply use public transit to reach these places, which are often located in moderately densely built areas. So, allow me to restate your claim, with a different assumption:
Of course you need great mass transit connections to a stadium, how else would people reach it?
Edit: But yes, people also don't have a good intuition on how much space cars actually waste in bulk. For example, many people don't seem to realize how much space it saves on roadways if 50 people sit in a bus or or tram or train rather than in 30 or 40 cars. Indeed, any rational motorist should be enthusiastically in favor of any project that makes public transit more attractive or accessible, purely for selfish reasons!
Or Letzigrund in Zurich, with a capacity of up to 50,000 people for concerts, and absolutely zero street parking available: https://goo.gl/maps/kPye3VdVB9ZLpPsx8
Edmonton's original light rail line was good for connecting the home of the Oilers with the home of the Eskimos, the former home of the Oilers, as well as the home of the Ooks, the Golden bears, as well as the Saville Sports centre and the Claireview rec center.
The light rail line is not so good for connecting people from their home to their place of work. It was built a long an old industrial rail corridor 40 years ago and the area around all the rail stations is still zoned as industrial.
They've since built massive expansions, which is good, although they are now nearly 4 years behind schedule on the first major leg expected to open. I'm looking forward to an lrt system that's good for more than getting quickly from one sports complex to another.
I'm also a little curious on how to compare capacities. Per wikipedia, it is only 25k for sports. 70+k for teams is common in many of the other stadiums I looked at. That said, I don't exactly know that many stadiums. Very intimidating to see how large many of these places are.
There are a few thousand parking spots in garages a few stops away on the light rail, but the whole district the stadium is in has only about 5k public parking spots overall for ALL purposes. The sensible strategy is to arrive by public transit — many of the events (both concerts and sports events) have a train ticket included in the price of admission, run extra trains for the events, (including extra security in the case of soccer games), and light rail drops you less than 100m from the entrance of the stadium.
If you absolutely need to arrive by car, either come early or pick a garage elsewhere in the city, and take public transit to the stadium.
If you're absolutely allergic to public transit, you could probably get a Taxi, Uber, or friend to drop you off.
For sports events, some of the away fans travel in hired buses which will drop them off at the stadium, wait at some special lot (considerably more space efficient than the equivalent in cars, and can be further away), and pick them up again after the game.
Even in US cities, stadia often lack massive surface parking lots. Giants stadium and Fenway are examples that do have some (very expensive) parking but are also on top of transit.
There is a tacit assumption in your statement. Of course you don't need vast parking lots around stadiums, and there are plenty of real-world sports arenas that don't have those (some examples [1][2][3]). The parking that there is is structural, and most people simply use public transit to reach these places, which are often located in moderately densely built areas. So, allow me to restate your claim, with a different assumption:
Of course you need great mass transit connections to a stadium, how else would people reach it?
Edit: But yes, people also don't have a good intuition on how much space cars actually waste in bulk. For example, many people don't seem to realize how much space it saves on roadways if 50 people sit in a bus or or tram or train rather than in 30 or 40 cars. Indeed, any rational motorist should be enthusiastically in favor of any project that makes public transit more attractive or accessible, purely for selfish reasons!
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[1] Nokia Arena in Tampere https://goo.gl/maps/3WmAxfA2pCXDre8p7
[2] Helsinki Olympic Stadium https://goo.gl/maps/BQhopp5kRtTrEDR79 [under renovation in the aerial imagery]
[3] Tele2 Arena in Stockholm https://goo.gl/maps/za3y6HfRvocjfZR37