Possibly those other methods would've made it clear just who did it. If a White Council member assassinated the ruling head of another supernatural nation, there'd be war.
Which kind of raises an interesting question. There's no White Court equivalent of the Lords of Outer Night or the Black Court Elders. Now, they can be extremely powerful by controlling mortals. But back 2000 years ago before mortal technology amounted for much (they've got to be older than that since they speak Etruscan), before the Accords... what kept them around? A relatively small number of Wardens could have defeated them handily, since pre-mortal-tech, they lack any ranged attacks to compete with what wizards have. They're strong and fast and good at healing... but wizards could burn them down from a distance.
Pre-death-curse Lord Raith might have had an instant-death-touch, but he still had to touch you... which doesn't amount to much because something that strong could kill easily if it got to touching range anyway. And armor or even skin-covering robes would probably protect you from it. It doesn't really compete with the paralyzing will attacks of the Lords of Outer Night, which can be used at a distance... and there were 13 Lords of Outer Night and the Red King, and only one Lord Raith.
Lara's likely at the upper end of White Court power except for pre-death-curse Lord Raith, and while she has impressive physical abilities, they're not THAT awesome. Just knowing exactly where to put his feet (Demonreach intellectus) lets pre-WK Harry keep up with her, so I can't imagine her being much more than double human speed.
The White Court simply can't compete with high-end magic users. Against something like Eb's super death magic and force effects or Harry's massive fire attacks or pre-bodyswap Luccio's laser fire attacks...