1. Less likely to be damaged. If you are escorting your car seat to the gate there will be less people handling it so the chances of it being damaged while traveling through the airport are a lot smaller.
2. Gate checked items are rarely lost! How many times has an airline lost your checked luggage or it didn't make your flight and it had to be delivered at a later time? Your airline losing your car seat would be a sure way to start your vacation off on the wrong foot. Sometimes airlines have car seats available for passengers in instances like these but it's not a guarantee and you never know the condition of the one they provide. If you are renting a car at the airport and that company rents car seats you could potentially get one if they have any available. However if they don't one person would have to get the rental and go and buy a car seat and then come back for you and your child. But what if you are traveling alone, then what? If you have a family member or friend picking you up they would now have to stop and buy one for you. If you planned on taking a taxi they most likely won't have one especially if not pre-ordered. In big cities like NYC, there is Uber Family but there are restrictions on children who can use the car seats they provide, most importantly that they must at least be one. Whoa that all sounds like a big pain!
3. You could get lucky and be able to bring your car seat on the plane! Even if you didn't pay for seat for your child under two if the flight isn't full you may be lucky enough to get a seat for your lap child. Get to the gate early and ask the gate agent if there are any open seats on the flight. If there are, let them know you are traveling with a lap infant and if that seat isn't already in your row if there is anyway passengers could be rearranged so your lap child could have their own and be seated in their car seat. To increase the chance of an open seat I always select our seats in the last few rows and seat myself in the window and my husband in the aisle. The rows in the back and middle seats always fill up last so if the flight doesn't sell out these are the seats that are usually open. The gate agents and flight attendants I have encountered on many airlines are usually more than willing to assist, the more comfortable your child, the smoother the plane ride for everyone. Just don't ask the gate agent to reassign seats if you get to the gate during final boarding!