What benefits do higher-rated NMR tubes provide?
A general rule is: crap goes in, crap comes out. A large-sample low-field 1D NMR at room temperature is usually only minimally affected by using a cheap NMR tube. There are important differences though and I’ll highlight a few.

The first distinction between prices is what the tube is constructed from: quartz obviously costs more than borosilicate. Why would a chemist ever use the more expensive quartz? You can heat/cool quartz faster (nice for thermal studies), the UV cutoff is lower (think 190 nm opposed to 320 nm) which is important for photolysis, you can work with quartz at higher temperatures (around 1300 °C instead of 250 °C), and the purity of quartz is better controlled than your typical Pyrex. There are different grades of quartz, fused and synthetic, and there are different grades of borosilicate, such as the high-quality Pyrex or the lower-quality Class B, each comes with its own limitations as far as purities are concerned and so forth.

Three more important parameters have to do with the manufacturing of your tube are: concentricity, camber and wall thickness. Lower quality tubes will tend to have less precision and accuracy over each of these parameters and as a result your sample may wobble while spinning (introducing problems such as modulation sidebands). A particularly bad tube can hit your RF coils and cause damage to your probe over time slowly or quickly if it is ignoring any reasonable standard – even more apparent for a tube at this level of “quality” is that it may be easier to break while acquiring your sample and we all should be aware of how much fun that is for everybody involved.

Shimming can deal with impurities present in the glass (such as ferric oxide) and increased impurities in the glass/inhomogeneities will result in taking longer to get a good shim. Time is money.

A lot of these things have lower tolerances in more complex experiments and at higher fields. It really does depend on your particular experiment and what you’re hoping to get out of it.