Why do some of the hosts on our home network drop when I change the transmission rate from auto to 130Mbps or 270Mbps? Is it because their wireless NIC can not support such rate?
Based on signal strength, which is a measurement that is constantly fluctuating and affected by many environmental factors that are out of your control, the maximum possible practical transfer rate changes over time.
If you force the router to only accept connections at a certain bit rate, you are forcing any nodes that are only able to communicate at a lower bitrate to be knocked off the network, either due to the hardware not supporting that speed, or signal strength.
Imagine you are in a quiet room having a conversation with someone. Now gradually start adding an increasingly loud background noise, like the sound of running water. Eventually when it's loud enough, even speaking in a loud tone won't be enough for you to be able to effectively communicate; you'll have to say "what?" and get them to say things twice or three times over before you can understand it.
Whenever signal strength decreases, a smart wifi node will adjust its max. line bitrate downwards, for improved stability. If you declare that your bitrate is lower, it's easier to reliably achieve that lower bitrate, i.e. the error rate will be lower, but if you increase the bitrate, you have more data going back and forth, and it's harder to keep track of all the errors, resends, dropped packets, etc. and it becomes really impractical.
Another way to look at it is that a reliable connection can still be made even on a "noisy" medium at a low bitrate, but in order to attain higher bitrates with any sort of reliability, you need to reduce the noise. When you have factors influencing your signal strength, noise can go up and reception goes down, and the only way to retain a stable connection is to reduce the line speed.
A few things that can temporarily drive down signal strength:
Bottom line is, just let the router and client negotiate a sane speed at any given moment, by keeping it on auto. That said, you could theoretically eliminate 802.11b/g, because 802.11n completely supercedes 802.11b/g, and contains all the speeds that 802.11b/g advertised. So you can take advantage of the improved protocol features of 802.11n but still allow the router and client to step down to lower speeds if they need to.
What you actually want to do is to disable the older protocols, which is a completely separate issue than setting the minimum speed to connect to the network. Your router's configuration page may or may not have a setting to explicitly disable b/g/a; if it doesn't have this setting, then just don't worry about it.