the realistic sample sqlite database I'm using
is over a gigabyte, and has 7.5 million records
in it's largest table.
It appears that you don't put any limit on the number
of records you try to count, or load into memory,
when browsing data.
Some reasonable (and flexible) limit should be
applied by default.
There probably is one and you just have not hit it yet, albeit, that is a rather large table.