Consider the positives and advantages of having your child compete in track.
At least your child actually gets to compete in track meets and you get to watch, even if they are not one of the best. If they were on a football, basketball or other team, the coach might never put them in the game and you would only get to watch them sit on the bench.
When your child does compete in track, you get to watch their entire race. This is unlike cross country running, xc or downhill skiing or even mtn bike racing where you might only be able to see them at the start, finish and/or maybe for a few other moments along the way.
You can cheer, yell and scream for your child at a track meet and there is a good chance they might hear you. There are normally not that many other spectators there making noise. Likely no other sounds to overcome as there probably will not be a marching band, cheerleaders or an announcer with amplified sound calling the race at a track meet.
Since there are normally not that many spectators at a track meet you can ger really close to the outside edge of the track and watch your athlete compete only a few feet away. If they are a distance runner you might get to see them pass very close to you many times. You should be able to get close enough to the edge of the track to see their facial expression and they might actually see, recognize and acknowledge you. In most other sports you can't get that close to the field of play and even if you can the field of play is much wider than an 8-lane track. Your track child's face in not obscured by a helmet, hat, water, etc.
Your child's track uniform is minimal and does not have a large number on it. This is in recognition of the fact that spectators like you will be able to easily identify specific runners by their face, hair, body etc. Track uniforms are minimal and track athletes expose more of their body and skin to the world than any other sport (swimmers may wear less, but you can't actually see their bodies in the water). As a parent you may get to see more of your child's body at a track meet than any other time. You can check for and evaluate tatoos, scars, development etc. without being confrontational
When your child is not actually competing on the track they can hang out with you (if they want to). They can come up into the stands or you can go to the warm-up area to talk with them. They normally could even come to your car with you during the meet to get different things or whatever. It is not like team sports where they have to be on the bench, dugout or in the locker room during half time and you can't get access to them.
If you are able to and your child wants to, you can often help them prepare for their race by warming up with them. You can jog with them, run strides with them, stretch with them, etc..often in an area outside the track itself. After their race, you could also warm down with them or help them prepare for their next race. As a parent you are never going to be allowed on a basketball court, football or baseball field during warm ups.