From my own random sampling of banks, I find the exact opposite - pulls generally have higher limits than pushes. This makes sense when you think about how the system operates.
A push puts the financial responsibility for fraud on the originating bank. Imagine account X pushes to account Y, and then account owner Y walks into the bank looking to withdraw cash. From Bank Y's perspective, everything looks fine. Later on, bank X finds out the push was fraudulent, but bank Y has relied on the transaction to dispense actual cash. Bank Y may help investigate, but they surely aren't going to be out the cash due to relying on X's false transaction.
Whereas the pull transaction (with Y as the originator), bank Y will put a withdrawal hold, scrutinize the cash withdrawal and ask if this is really their customer, etc, since there is no other party they can blame.
I also personally tend towards using pulls because that's the way the system expects to work since it grew out of checks. If one pushes money and it never shows up, then the blame is ambiguous. From the originator's perspective they've completed what you've asked them to do, and from the receiver's perspective they know nothing. Whereas with a pull, the main thing you're doing is asking the originator to credit your account. If the transaction gets lost without your other account getting debited, then the discrepancy doesn't really affect you.
A push puts the financial responsibility for fraud on the originating bank. Imagine account X pushes to account Y, and then account owner Y walks into the bank looking to withdraw cash. From Bank Y's perspective, everything looks fine. Later on, bank X finds out the push was fraudulent, but bank Y has relied on the transaction to dispense actual cash. Bank Y may help investigate, but they surely aren't going to be out the cash due to relying on X's false transaction.
Whereas the pull transaction (with Y as the originator), bank Y will put a withdrawal hold, scrutinize the cash withdrawal and ask if this is really their customer, etc, since there is no other party they can blame.
I also personally tend towards using pulls because that's the way the system expects to work since it grew out of checks. If one pushes money and it never shows up, then the blame is ambiguous. From the originator's perspective they've completed what you've asked them to do, and from the receiver's perspective they know nothing. Whereas with a pull, the main thing you're doing is asking the originator to credit your account. If the transaction gets lost without your other account getting debited, then the discrepancy doesn't really affect you.