What the Governor-General (Francis Rawdon, Earl of Moira; later Marquess of Hastings) wanted in 1814 was not the daily headache of annexing the highlands but the commercial and strategic value downstream of them. His own journal cuts through rhetoric: Kumaon as a hinge to "Tartary" (the British phrase for Qing domains) and a monopoly on shawl-wool routes stands out as a primary lure.
Company paperwork from the war years presents a matching picture: Papers Respecting the Nepaul War (1824) collates proclamations, letters and memoranda used to justify policy—security along the Tarai, access to hill passes, and the need to regularise a fractious frontier.
British usage of "Chinese Tartary" in Himalayan writing of the era underlines the trans-frontier logic, not a desire to push the British Raj into the high Himalaya. The routes and markets beyond the crest mattered; permanent occupation of the crest did not.
Bottom line
Annexation was unnecessary to those aims; control by treaty, roads, residency, and recruitment was cheaper.