GNU split
Use GNU split with its --filter option:
seq 100 | split -l 10 --filter='wc -l'
Note the value for --filter= is interpreted as shell code, so you can directly build more complex logic there; and split sets a variable named FILE for you to use. Example:
seq 100 | split -d -l 10 --filter='printf "%s: " "$FILE"; wc -l' - 'chunk '
GNU parallel
While split runs filters sequentially, GNU parallel can start many jobs in parallel. With seq 100 and wc -l this is overkill, but for more complicated jobs parallel makes sense.
seq 100 | parallel --pipe -n 10 --keep-order --group -- wc -l