With regards to the battery type used, I think it's very appropriate to the design of the binocular. CR123 requires a significantly larger housing that the CR2 and AA (format) is really out of the question due to length. Compromises have to be made when attaining IS is this size. If a person is going to "bird all day" I think you're probably right, the binocular might not be for you. If you don't mind replacing the battery in the field, there's probably no reason that it couldn't be an "all day" birding bin but how many people are using a 10x25 as their primary / "all day" birding binocular, regardless? For many people, a larger EP and brighter image are preferred.
I've seen no actual "run-time" test associated with this model but it's safe to say that the stated, 3-3.5 hours of stated runtime is probably over stated. Manufacturers typically report best case scenarios when it comes to battery life and duty cycle greatly effects battery life. A continuous discharge from a Li CR2 will result in much shorter run-times than when used for 1 minute increments , spread over a 12 hour period. I have many flashlights/torches in the CR2 format and run-time varies wildly with duty cycle, even at lower discharge rates.
With regards to the stated capacity of rechargeable 3.0V Li-Ion CR2's, they will never have the same energy density as CR2 3.0V Lithium (primary) cells from Duracell, Energizer, Panasonic, Sanyo, which have an actual capacity of 750-850mAh. Rechargeable, Li-Ion 3.0V CR2's (different chemistry than lithium) have an actual capacity of 300-400mAh. I realize that examples were given of advertisers on Amazon claiming 800mAh capacity for these rechargeable 3.0V li-ion's but these manufacturers.... all Chinese, can print any capacity number they want to on the cell and it doesn't mean anything. While there's no central point of reference data for these Rechargeable Li-ion 3.0V cells, the various flashlight/torch forums are your best source, when trying to determine actual capacity.
The point of all of this is to say that if you are going to use Rechargeable Li-ion 3.0V cells, expect run-times that are about half of what they are for the standard CR2 Lithium. There's no free lunch and your giving up performance to use the rechargeable 3.0V cell.
The most important part: Please do not mistake these non-standard, Rechargeable 3.0V Li-Ion cells with standard 3.7V (nominal) Li-Ion, (4.2 volt max) cells, which will likely exceed the rated voltage of devices like the Nikon. If you don't know the difference, don't take the chance and just use standard, non-rechargeable, CR2 Lithium cells from Duracell, Energizer, Panasonic and Sanyo.