You made a great observation there and you are correct in general. Fortunately the effect is incredibly small for football fans in Jacksonville. Let's walk through it to see:
The population of Jacksonville is 892,062 (according to Google). By the probability in your survey 72% of them are football fans. So that gives us 642284.64 football fans (we're going to round to 642285 fans because well 0.64 fans is awkward).
So considering your reasoning the probability of the first person sampled being a football fan is: $$642285\over892062$$
The probability of the second person being a football fan is then: $$642284\over892061$$
If we multiply those together we get 0.51840035513 as opposed to 0.51840058112 from the original calculation. So the probabilities differ by 0.00004359372% which is pretty insignificant for an example problem.
So where does this become important: well let's say the population of Jacksonville is only 4 people and 3 of them are football fans. According to the textbook the answer for finding two football fans is $0.75^2$ or $0.5625$. While by your observation and the correct model it is $0.75*0.6666$ (3/4 * 2/3) or $0.5$. So now we have more than a 10% difference between the two answers.
As the population shrinks (either of football fans or of people in total) this consideration becomes ever more important. What's the probability of finding two football fans in a city with a population of 2 where 50% of them are football fans? Well the approach the example uses would give $0.5^2$ or $0.25$ while the correct approach gives 0 (there's only one football fan so you have 1/2*0/1).
What you have stumbled across is the difference of sampling with replacement vs sampling without replacement: https://web.ma.utexas.edu/users/parker/sampling/repl.htm