They don't want the precedent established. Same reason why uninvolved parties in US courts submit "amicus briefs" - the precedent from a case may affect them down the line.
The US doesn’t believe universal jurisdiction applies to it or its vassal states and proxies, which includes Israel.
On the other hand, the US didn’t try to prevent Slobodan Milošević from being tried at The Hague for war crimes and genocide, as Serbia wasn’t a vassal state or proxy.