Difference between Antenna and Filter
Your assumption seems to be that filtering only one time is enough.

That might be true but it might also not be true, it depends factors like:


How much filtering outside your band of interest is needed? If there are strong signals present at frequencies you do not want, you might want to suppress these as much as possible before they end up (with too much power) in your receiver.
What is the quality factor of your antenna, it might not filter as well as a dedicated filter. In some situations you might even want an antenna that is quite broadband, so receives much more than you want and then filter out the band of your interest with a filter. Why would you want a broadband antenna? It might be that the antenna is influenced by its surroundings. For example in a mobile phone, there's the "hand effect" which means the antenna is de-tuned when a (human) hand is nearby, holding the phone. You would still want the antenna to receive the signals so it should not be de-tuned too much by the presence of a hand.