Hand-counting certainly is possible, and there are places in the US where it is still the regular process. However, besides the high cost of bringing on a sufficient number of temp employees (additionally complicated by the typical requirements that ballots be counted under supervision of both major parties), it's a real concern on the mind of election officials that hand counting is appreciably less accurate than automated tabulation. It's possible to multiply count ballots (e.g. count each batch twice and average results) but the general attitude is that ballot counts must be absolutely correct and any discrepancy prompts a complete recount. This results in a need to have each ballot individually entered by two people and compared one-for-one... the process is quite time consuming even for the relatively small number of ballots that are hand-counted in this jurisdiction due to damage that prevents the tabulators accepting them.
Finally, there is the simple problem that the voter is not able to see their ballot tabulated "before their eyes," which is standard enough in most US jurisdictions that voters can get frustrated or worried if it isn't the case (e.g. due to a provisional ballot where the registration must be investigated before it can be tabulated, something that is thankfully becoming uncommon due to same-day voter registration). Once you're used to casting your ballot and "waiting for the ding and green light," it's a bit worrying to see it just stuffed in a canvas pouch.
This definitely isn't a problem that can't be overcome, but I think to some extent comes down to the culture of election administration, which is that everything must be absolutely correct to the individual ballot, and as much as possible should be done directly in the polling place (since that's where most of the independent observers/challengers/scrutineers are located).