We flew United from Narita, with a 1 hour 15 min layover. We were scheduled to leave NRT at 16:10, and arrive at Dulles D gates at 15:50. By the time we got off the plane, it was about 16:00. When we got to customs, there were several hundreds of people in line, all bottlenecked by just 3 agents working. I understand these are two of the busiest times of the day at both ends of the journey, but surely United knows this too, and surely they have an obligation to schedule accordingly. There was some weather delay at Narita, and so our connection time was even shorter. We got through customs and scurried to C concourse at 17:05, the scheduled time for our departure, just in time to see the flight leaving on the schedule board. We were on the hook for overnight expenses, not United, they told us, because it was Narita's fault. Really?? Nobody at United had 12 hours to make sure there would enough customs staff to get us through on time?
No. One and a quarter hours is a very very tight and unreasonable connection for an international flight with a stopover going through USA immigration whether on one ticket or multiple tickets. That would require both connecting flights be on schedule and smooth passage through customs and immigration.
In the race to maximize profits and please Wall Street, air travel (particularly in the USA) is going to the dogs. Although the contract does not stipulate they have to accommodate you overnight, legacy carrier airlines typically used to do that as a courtesy to their clients but are now now skimping on it.
Call their frequent flier customer service line and complain politely but vigorously, they’ll probably gift you some miles. Better still if you’re on social media like Twitter, let them have it there and they’ll pay you off (miles or voucher) to silence you
Nobody at United had 12 hours to make sure there would enough customs staff to get us through on time?
Of course not. Customs and immigration is run by the US government. United (or any other airline) has almost zero control over staffing levels, shift schedule, etc.
We were on the hook for overnight expenses, not United, they told us, because it was Narita's fault. Really??
Here are United conditions (to which you agreed, when you booked the flight). https://www.united.com/ual/en/us/fly/travel/flight-delays-and-cancellations.html They are responsible for expenses for a missed connection if they are at fault. This specifically excludes weather and immigration/customs is kind of a gray area.
All airports/airlines have minimum connection times which are based on statistics, i.e. most flights & people will make it within this time. But that's never 100% since there are always things that can go wrong and connection time vary a lot with unpredictable factors.
In the end, the passenger has to decide what level of risk they are comfortable with in exchange a convenient connection. If you have Global Entry, TSA precheck, and no checked luggage, you can tolerate a much shorter connection than if you have a passport from "difficult" country and lots of heavy luggage. The airline can't know this, when they create the flight plans, so they need to go for "average".
1 hour 15 min is a reasonable time to make an international connection at Washington Dulles - if you have (for example) Global Entry (and thus PreCheck) and no checked baggage. It is absolutely NOT a reasonable time for (for example) a foreign visitor with checked baggage and no PreCheck.
As this is a reasonable connection time for some customers, the airline allows you to book such a tight connection. That doesn't mean that you should do it - it just means that they allow it.
As the airline allows you to book a tight connection, they will re-accommodate you on a later flight if you do not make your connection. Technically as your inbound flight was (seemingly) on time, they technically have ZERO requirement to do this, but United (and most other US airline) will do it as a courtesy. Given that there was no delay, the airline will NOT be responsible for covering additional expenses like accommodation, however it is possible that your travel insurance will (you do have travel insurance, right?)
IF the inbound flight had been delayed, then the story would be a little different. Depending on the class you were travelling in (eg, Business v's Economy), your Frequently Flyer status, and the cause of the delay the airline may have provided a hotel and meal vouchers.
Your specific complaint about the number of "customs" staff is irrelevant - the number of staff working is controlled by US Customs and Border Protection, not the airline. CBP actually publishes detailed information on wait times at all airports on their website. A quick look at this shows that it's not uncommon to wait up to an hour or more at the times you're talking about.