30 years ago when I wanted to play an instrument in grade school we also had to test. If you wanted to play a woodwind you had to show you could actually get the mouthpiece to make noise. If you wanted a brass, same thing. I couldn't get the flute mouthpiece to play but was able to make the reed work on a clarinet mouthpiece so I got the clarinet.
Everyone at my school wanted flute, sax, drums, etc. I got the oboe. I'm not sure how much babysitting money I spent on reeds for the darn thing, but in 9th grade I was asked to play three solo's for the school spring concert. I also got to play bassoon and xylophone, which were both interesting.

You band didn't have a single horn? That stinks. Not that your daughter should be forced to do so. It's just sad.My daughter wanted to play the flute in junior high marching band. The band director assigned her the French horn. Of course, we were expected to buy her instrument. Buy a French horn? I think not. She played the flute. Nobody played the French horn. The band got along just fine.
I started Clarinet in 5th grade in Nashville TN. We had a lot of clarinet players that year and there were only two flutes. I often was relegated to drums since we needed more percussion and we had so many clarinets.
The next year we moved to NC. The schools there started band in 6th grade so I got to choose all over again. I decided on Flute since not many people played it. Wrong. There were more flutes than any other instrument that year. Can't win.
Count me as one of the kids who didn't do band because I couldn't play the instrument I wanted to play. I wanted to play clarinet but they told me I had to play trumpet - I didn't want to so I walked away. This was in sixth grade. Oh well - I joined the dance team instead so it's not like I was scarred for life but still...
I am an elementary string teacher and go through the same recruiting process. I am married to a percussionist (high school band director) and one of my sons is a percussionist. I also have a clarinet player, a violinist and a trumpet player.Back story - the school DD10 attends does a weird thing with band. Rather than letting the kids choose their instruments, they "test" all the kids on everything & assign them an instrument. The test consists of about 30 seconds of each instrument.
Knowing this & also knowing DD wants to play drums, we put her in drum lessons over a year ago. So, tryout day was Friday & of course she scored highest on drums.
Band director approached DW this morning & said she thought DD would be "bored with band because she was too advanced on drums" and she suggested DD take up another instrument for at least a year......
Facepalm
Just wondering is this also the type of school that usually sells or rents the instruments to their band members? Maybe they are pushing her to try something else so that they can sell you the package. I remember my band director being very upset that my mom had already bought me a clarinet. I tested fine for it (I knew the test before we bought it as my 2 older brothers were already in band at that point) and was allowed to play but he kept pushing for me to do something else and it came out that it was because they took cuts on instruments they were able to sale.