Self interest not ideology is driving Iranian allies involvement in Gaza war

Since Hamas attacked Isr on the 7th Oct, there has been speculation about Iran and its allies motives of involvement in the ensuing war with Isr. On the face of it, they claim their involvement is driven by their religious backing for Pal and to pressure the US to stop the war. Below the surface, however, this driver seems weak given the high risk taken in this venture. The reality is more strategic and defined by self interest. 

In Lebanon, Hezbollah is seeking to liberate its occupied territories from Isr by pressuring Isr military in its northern borders. In Yemen, Ansarallah is trying to break the maritime siege on Yemen by demonstrating its ability to blockade Isr. In Iraq, Iran allies are seeking to push the US troops out of Iraq. This is expected to also pressure US withdrawal from Syria which is dependent on US military presence in Iraq. Iran itself is using this war to show power and influence in reaction to last year's regime change attempt. The regime has now regained broader domestic and regional legitimacy. 

Overall, driven by self interest, Iran and its allies continue to be heavily invested in the war and they are likely to carry it on until the end. As a result, some of these objectives will likely be achieved by the end of the war.