A short answer would be:

They tried. However, Hannibal's strategy was to show to Rome's allies in Italy that Rome could be defeated and thus to allow them to gain independence. In this, he almost succeeded. Yet, Rome did integrate their allies in a much tighter ideological way than Carthage did, which made them reluctant to rebel as many felt to be Roman themselves. In addition, Hannibal didn't have enough troops or siege equipment to siege Rome and Carthaginian reinforcements were intercepted by Rome's navy I believe. It went downhill from there and barely anyone expected that Rome would be able to recruit, equip and field one capable army after another after each defeat.

For longer answers, discussing many of these points including Hannibal strategy, see e.g.:

https://www.reddit.com/r/AskHistorians/comments/kofimg/was_hannibal_a_bad_strategist_despite_being_a/ghs2191/ from /u/dandan_noodles

https://www.reddit.com/r/AskHistorians/comments/iyvtx6/why_didnt_carthage_afford_hannibal_the_aid_he/g6jabdp/ from /u/Suffet_Menander

Edit: Somewhere, there is my answer about organization differences of allies and their integration with Rome and Carthage respectively, which could give you a bit of perspective. Sadly, I can't find it.