May implement local payment support via OmniPay library (http://omnipay.thephpleague.com/gateways/official/). If we do that put a note in other payment gateway issues that OmniPay supports as now supporting local payments (but payment button work may still be desired), and document.
No application needed: Yes
Transparent pricing: Yes
No monthly fee: Yes
Reasonable per-transaction percentages: Kinda (3.5%, 4.5% for subscriptions)
No bad reputation: Yes
Targets micro businesses: Yes
Payment button+IPN API: Yes (https://verifone.cloud/docs/2checkout/API-Integration/2Pay.js-payments-solution)
Local payments API: Yes (https://app.swaggerhub.com/apis-docs/2Checkout-API/api-rest_documentation/6.0#/)
Reasonably modern website: Yes
Reasonably stable business: Yes (Verifone)
International: Yes
No bank merchant account needed: Yes
Supports subscriptions: Yes
Supported by PHP Omnipay library: No