Agree, if the instrument sounds awful or won't stay in tune a student will get frustrated. But there are good musical instruments which should be affordable to those on a limited budget. Just research options from the name brands. Just considering Diatonic lines there are a number of good options in harmonicas across the price spectrum. Looking at just the Hohner brand a Marine Band or Blues Harp are made in Germany and have a great rep, but then Hohner also has the Hohner Blues Band which is much less expensive but made "elsewhere". Lee Oskar is another brand with a good rep. Unless your ears are trained it probably doesn't matter. If you are on stage and getting paid it probably matters a lot.

When it comes to recorders (aka common flute) the price range is crazy. Unless I was a professional, who really needed and could play well enough to justify the expense (time & money), there is absolutely no rationale for buying anything in triple digits (wood). Wood recorders tend to be expensive to buy and are more finicky. You need to keep proper moisture levels in the wood and oil them as you would a fine piece of furniture. OTOH, there are name brand recorders that are affordable and sound great, but they are plastic. The youtube videos linked above address this issue in detail. Still, $30 for a good one, $40 for a really good one -- both will last a lifetime -- play it every day, don't play for years, doesn't matter. Stick one inside your backpack and don't be concerned.