I highly disagree that Iran’s allies did the wrong thing by intervening in this war. It made strategic sense.
Exactly the opposite is true.
Hamas is a managed threat cultivated by Mossad as a political counter to Fatah. Fatah was a problem because they formally agreed to a two-state solution along 1967 borders which became the foundation of Oslo accords. To prevent the formation of a Palestinian state Israel fostered Hamas (interestingly: as an Islamic jihadist organisation first, and Palestinian nationalist organisation second) as a "honest" option to Fatah's "collaborators" within the Palestinian Authority. This meant that Israel could then sabotage the negotiations by imposing unacceptable conditions to which Fatah would
partly agree and which Hamas would reject on principle. This split the population sufficiently that Fatah could not govern alone which in turn meant that Palestinian autonomy had no path to legal sovereignty.
This is why Hamas could exist for so long and operate with such impunity despite having no credibility as a jihadist organisation and very little support among Arabs, as well as being listed as terrorists by Egypt due to Hamas' links with Muslim Brotherhood. This last thing is absolutely fundamental to understanding the true nature of Hamas because with Egypt's openly hostile attitude to Hamas it was impossible to maintain its presence in Gaza without help from Israel.
So for Israel to eliminate Hamas would be a net gain for everyone opposed to Israel. This is why any involvement in the conflict - whether explicitly or implicitly - on the side of Hamas was a strategic mistake. Israel would have to either fail to physically eliminate Hamas - which would be politically untenable in Israel - or it would remove a competitor for funds and attention.
The inevitable need for occupation of Gaza - which follows from Israel's intention to displace Gaza's population and annex the territory - meant that the reaction against Israel could be delayed to after Hamas was eliminated. It would force Israel to manage the entire show without external help which would skew the optics further against Israel as well as force them to justify being less effective despite lack of distractions.
Hezbollah, Houthis and other Shia forces have no obligation to help a Sunni force that is considered to be a bad faith actor. They reacted because they are not nearly as competent as their propaganda claims.
If there's one constant in Arab-Israeli wars it is that Arabs have always great propaganda that is always contradicted by their results. You're making the same mistake as if the previous 75 years taught you nothing.
Only way Israel can do anything about the north is a full scale war which they cannot win.
Israel can easily win the war against Hezbollah provided they go all in which is why there is such pressure from Netanyahu's faction. IDF is resisting the war only along political lines, not strategic ones. They understand the consequences so they oppose and support the operation based on their political stance in Israeli politics, not military assessment.
Objectively this is the best moment for Israel to attack Hezbollah precisely because it is the worst moment for Iran to become involved and without Iran Hezbollah is significantly weaker than it claims to be on paper.
Militarily Hezbollah is not self-sufficient and Iran has made sure of that because otherwise they would became to difficult to control and would no longer be useful as Iran's conventional deterrent. It would become similar to the Houthis and the Houthis while useful to Iran are at the same time a problem. For example Houthis' reckless campaign against shipping while not directly targeting Chinese trade it nevertheless impacted Chinese trade indirectly through economic and legal fallout which is problematic for Iran's relationship with China.
There is also one major drawback that emerged from Hezbollah's slow evolution from an underground irregular force that it was in 2006 into a state-level actor that it has become now. The closer Hezbollah is to peer warfare with Israel the easier it is for Israel to degrade and disrupt its operations, especially if Israel is given sufficient time to perform recon and strikes against key targets. And that is exactly what Hezbollah has done for the last year.
After 7 Oct game theory presented only two good solutions for Hezbollah - either stay out of the fight and hide its movements or attack as soon as possible with full potential. Anything in between worked to Israel's advantage and Hezbollah has spent a year doing just that.
Hamas was never the problem for Israel - as indicated above. Hamas was a convenient ploy to set Israel on a collision course with Hezbollah.
Furthermore Hezbollah is presently in an extremely precarious position in Lebanon having far less overt political support in the country than it is claimed in propaganda. Hamas has only 15 out of 128 seats in Lebanese parliament, and only two ministerial positions. Every other faction - including Shia party Amal - is hostile to Hezbollah. The only reason why Hezbollah maintains its current political position are the the internal divisions between Christian factions in Lebanon. If Christian factions cooperated then with help of Amal they could appeal for aid in removing Hezbollah from Lebanon. However as long as the individual factions are more interested in growing their own political and economic fiefs outside of the de facto failed Lebanese state structure Hezbollah is not threatened due to their military potential.
Israeli intervention in Lebanon, especially if Israel's western allies are involved - even if just politically - could provide the impulse to temporarily realign other factions against Hezbollah. In such scenario Israel takes over southern Lebanon and deals with militant Shias while the rest realigns itself to a new political architecture with significantly strengthened Christian position. That in turn will absorb Iran's attention as it will attempt to salvage its position in Lebanon (and Syria).
Yes there will be a high cost imposed on Israel as a consequence of their invasion but the entire year has been a trial run for that operation. Netanyahu is going full Hitler only with more preparation and because of that economic or political costs are of no importance while potential gains are of tremendous value. And they are by no means far fetched. If IDF chooses the correct strategy they have extremely high chances of success and all of that will be the fault of Shia factions which foolishly uncovered their cards too early in the game.
This is the most expensive war in Israeli history.
1948-49 and 1967-1973 were far more expensive in real terms but the gains changed the calculus. Netanyahu is hoping for the very same thing as this is his ticket to political immunity as a once-in-a century national hero. It's an all in game and likely has been from the very beginning.