Is the checksum used in BIP39 mnemonic sentences too short?
Checksum in BIP-39 is mainly used for padding which may be the reason why smaller size checksums are used.
Each BIP-39 word represents 11-bits and in order to divide the entropy of an arbitrary size (which is normally a multiple of 8-bit such as 128, 160, 256,...) to 11-bit chunks it has to be padded first. For example in case of a 128-bit entropy 4-bits padding is needed (128+4=132%11=0) and that pad is the checksum.
BIP-39 authors may not have thought about recovery cases but if a bigger checksum were to be chosen it has to pad the total length to a multiple of 11. In case of 128 bits it needs to be 15-bits (128+15=143%11=0) or 26-bits, 37-bits,...