As far as I understand, different command-line interpreters (the Linux console, the bash shell, busybox…) translate these keys (Insert, Delete, Home, End) to key-codes in different ways, and then the underlying programs (aterm, urxvt…) interpret these key-codes with some variations. All of this makes for a rather fragile process. If the terminfo database is up-to-date on your system, this shouldn’t be an issue. However, TinyCore Linux doesn’t seem to even have a terminfo database.
That is why “bash”, or rather the “readline” library that “bash” is using, fails to correctly handle the said keys. But “readline” can be taught.