All your old deposit addresses are always valid so you can deposit to as many of them you wish to in a 24 hour period. That means we have to monitor ~40 million addresses. The restriction on creating new deposit addresses was introduced because some idiot programmed a bot to just sit there generating new addresses.
The site could allow the user to create a new address, if at least one deposit has been made to a previously created address. It'd better for your users privacy if they could send bitcoins to different addresses because they wouldn't have to combine UTXO from different sources.
Definitely, you wouldn't want people from around the world to start hunting you down if you win the lottery 
There are thousands of people who own more than that, unless the winner lives in a crime-ridden country, he shouldn't have to worry over someone knowing he owns 20 bitcoins. (but there are reasons other than security to maintain privacy though)
I reckon it would be better if you offered multiple smaller prizes, but still something desirable to reduce the cost of the prize for the site. (Something like electric scooters or cheaper electric cars.) 
