It's not a funding issue, it's a deliberate political mismanagement issue.
Karachi didn't vote for PPP but a lot of Sindh did (mostly because it's under the thumb of PPP feudal lords) so Karachi ends up with a PPP pronvincial government. The government doesn't spend very much money there (no need, it's electorate doesn't live in Karachi) and rather embezzles the money in age honoured tradition of PPP. In rural areas they also don't spend anything, keep people poor and desperate, but often will pay family heads and local influential people money to garner votes for them at election time, or offer the family members of such people jobs in government as a "reward" for wrangling the votes of the poor.