Israeli Police Find Ancient Coin

Does Israel really think that most people finding these coins/relics would hand them in without compensation. That would be pretty naive on their part. Unless they do compensate - but I'm not sure of that

Israel's laws are less punitive than some other jurisdictions.

If you find an antiquity (defined in Israeli law as anything older than AD 1700), you are supposed to report it and have it examined. All such antiquities belong to the State. If the examiner determines the State doesn't really want or need it, the finder may be allowed to keep it. If they keep it, they are not allowed to sell it to someone else if neither the buyer nor seller has a permit (and it's my understanding that Israel hasn't issued a new antiquities trading permit in decades). So if you want to sell it, you're basically forced to sell to one of only a couple of dealers in Israel with the permit. Exporting them is of course also illegal without the permit, so you can't just slap it on ebay.

So if you find an old coin, you must report it. The authorities who examine the coin might let you keep it, or they might acquire it for the state if they deem it to be historically significant. And yes, Israeli authorities tend to deem all First Jewish Revolt coins as "historically significant", so you're not likely to be allowed to keep one of those if you find one.

As you can probably tell from the undertone in the OP's linked article, archaeology in Israel/Palestine is highly politicized - with the Israeli archaeologists seeking to promote the ancient landholdings of the Jews, and Palestinian archaeologists seeking to downplay such finds and promote non-Jewish archaeology instead. Thus, every scrap of stone, every shard of pottery, and every ancient coin potentially plays into that conflict. Especially if such artifacts are found in a contested territory, such as Jerusalem.

Israel no doubt strongly emphasizes this fact to it's citizens. Illegally digging up, keeping, selling or exporting a Jewish Revolt coin isn't just illegal, it's unpatriotic - you're actively helping The Enemy when you do that.