This is not as clear as you say. "No proof" and "no evidence" doesn't mean it didn't happen. Hamas controls Gaza with an iron fist. They are the ones carrying guns. They have no qualms about torturing, threatening, executing anyone who doesn't tow the line.

Hamas didn't just steal all the aid and put it in its tunnels. Hamas exerted influence by controlling the aid and its distribution. It did also steal some of it. You are to some degree misrepresenting the Israeli concern. Israel isn't simply concerned about Hamas stealing all the aid, it is concerned both about stealing and reselling (which does happen) and about control of the aid as means of continuing to establish itself as the governing body of Gaza. The UN agencies have and do work with Hamas in Gaza since nobody can be in Gaza without working with Hamas.

The NYT article is doing some hair splitting: "Over the course of the war, the Israeli military released records and videos purporting to show how Hamas has been exploiting humanitarian aid. The army also shared what it described as internal Hamas documents found in a headquarters in Gaza, which discuss the percentage of aid taken by various Hamas wings and dated to early 2024. But those documents do not specifically refer to the theft of U.N. aid."

"Hamas did steal from some of the smaller organizations that donated aid, as those groups were not always on the ground to oversee distribution, according to the senior Israeli officials and others involved in the matter. But, they say, there was no evidence that Hamas regularly stole from the United Nations, which provided the largest chunk of the aid. A Hamas representative did not immediately respond to requests for comment." - I like that last bit.

Your Reuters article also says: "A State Department spokesperson disputed the findings, saying there is video evidence of Hamas looting aid, but provided no such videos. The spokesperson also accused traditional humanitarian groups of covering up "aid corruption.""

and: "The study noted a limitation: because Palestinians who receive aid cannot be vetted, it was possible that U.S.-funded supplies went to administrative officials of Hamas, the Islamist rulers of Gaza."

Also:

https://www.timesofisrael.com/ex-us-humanitarian-envoy-pans-...

"Satterfield said “there’s no question” that the terror group has worked to take “political advantage and certainly some physical substantive advantage out of the aid distribution process.”

Hamas operatives have made a point of “flaunting” their presence at aid sites in a message to Palestinians that the group has no intention of ceding its role in the distribution process.

However, Satterfield maintained that “the bulk of all assistance delivered by the UN and by the international organizations has gone to the population of Gaza and not to Hamas. Full stop.”"

These are not contradictory, Hamas controlled the aid, but still the bulk of it got delivered. The problem is the control they asserted. Israel has tried, via GHF, to take them out of the loop. Nobody is disputing that when aid was flowing in it did eventually end up reaching the people (who sometimes had to buy it).

Of course there's no proof, how could it be proven??

But what's undisputed is that it wasn't getting through. From the UN itself:

https://app.un2720.org/tracking/

Of what entered Gaza only about 10% made it where it was supposed to go.

I think the most common string of arguments is that Hamas steals all the food being brought into Gaza, causing extreme food scarcity. Then Hamas corners the market on all food, raises food prices with its monopoly, and extracts big profits from the rest of the Gaza population. The claim, in conclusion, is that well-intentioned aid organizations bringing food into Gaza to feed starving people are actually funding Hamas.

The argument has proven totally wrong, because as every single humanitarian organization that operates in Gaza has repeatedly warned in recent months, famine conditions are the direct result of Israel generally disallowing food and other aid into Gaza since March. Had Hamas actually diverted billions of dollars into their food storage tunnels, then logically they would've continued selling it at market price when demand is high now. But actually in reality, there's nothing to buy. [1]

The market solution to prevent Hamas from profiting off food is to first allow in enough food to Gaza such that babies are no longer starving to death, and to then bring in so much food supply that prices decrease until it's no longer economically profitable to resell food, because it's widely available. That solution is never brought up for some reason.

[1] ‘There is nothing to buy’: Gaza’s descent into mass starvation https://www.ft.com/content/e5d7bcbb-4c9d-47b8-b716-6bd58ad57...