What are the strategies/thoughts in the industry? Holding and batching payments on a per-user basis? Trying to get agreements so you can batch payments on a per-processor or per-network agreement? Hourly? Daily? Weekly?
That's pretty much the story :-). And so the questions are then whether we subsidize the transactions, batch them (as you say, though that makes refunds and statement descriptors tricky), get card networks to change their policies, or somehow shift how the payments are made (e.g. encouraging cheaper payment methods).
The various US credit card & processing companies have an extraordinary thing going for themselves. Visa and Mastercard have cartel-like margins (Visa's operating income margin for 4Q19 was 66%, you don't see that outside of maybe illicit drug operations or Facebook's monopoly in its earlier thinner incarnation pre-Russiagate). They're super sensitive to giving any ground on their fee levels, out of fear (correctly so) that they'll never get them back.
Before the market drop, Visa was worth more than all publicly traded banks in Europe combined (frankly that may still be true post market drop, as Visa hasn't declined all that much).
Visa etc are now only allowed to charge a percentage, 0.2-0.3%, but the intermediate (Stripe etc) can still add a flat-rate fee.
If Stripe were willing to allow third parties to act as a batching passthrough (or if I was wrong and you do!), this seems like a low-cost way to let the market decide what an acceptable refund/statement descriptor regime should look like.
Maybe batch them per user per website, that will solve statement descriptors a bit
Payment requests are accumulated and batched, combined with "capping" of travel costs (eg max/day, weekly discounts etc).
I haven't used a debit card in years to maximize benefits (altho I sometimes use cash when required by small businesses), but the Capital One debit card advertises $0 Fraud Liability https://www.capitalone.com/bank/debit-card/.
This also makes me more aware of my spending, since I need to manually keep topping up the account.