Best option to index an application log table for quick insertion and retrieval in date order?
I think that's good, because it lowers page contention (vs inserting them all on the last data page all the time), but I'm not sure about that.

At insert rates of under 10,000/sec hot page latch contention is not a big issue, and the efficiency and locality of end-of-index inserts is preferable.


Change the primary key to be composite on (started, id) so it's the only index and the data pages are in order by date


Yes.  Prefer the solution where you don't need two indexes.  And look here for a solution to using a datetime2 as the only unique index on the table by filling the sub-second precision with values generated by a sequence.