Big banks are working hard to deal with the threat of disruption, and increasingly the local branch is a touchpoint that many customers are avoiding.

According to a new study by customer experience management firm Clarabridge, 36% of banking customers in the US haven’t visited a branch in the past month.

Instead, they’re banking online, with 38% using a mobile device to do so and another 35% using a desktop or laptop.

Given the reputation of big banks, that might lead one to believe that they’re in trouble.

But Clarabridge, which polled over 2,400 US residents between the ages of 18 and 59, surprisingly found that more than three-quarters (78%) of those using mobile banking are satisfied with the experience they’re being offered.

The biggest complaint about mobile banking is that it’s difficult to transfer money between different banks, but despite this, 42% of respondents prefer to use their banks’ app to transfer money while just 26% prefer to use a third-party app like PayPal or Venmo.

This preference is even present when looking specifically at millennial banking customers.

Is the fintech threat overblown?

The figures throw into question the notion that incumbent banks are at imminent threat of losing large numbers of customers to online and mobile-only upstarts like Mondo, which is luring customers with a slick app and raised £1m in a record-breaking crowdfunding campaign

Indeed, early efforts in the UK to encourage bank switching have failed to produce mass exoduses, and while studies show that millennials are more willing to consider a bank change, including to an online-only bank, they also overestimate the difficulties involved, suggesting they might not be switching at as high a clip as they otherwise would.

But established banks shouldn’t take their customers for granted, because the trends are not all favorable.

First, in a 2015 Accenture study nearly 80% of consumers indicated that they viewed their relationship with their primary financial provider as being transactional, not relational, and over half sought out other providers for loans, financial advice and brokerage accounts.

Unbundling is one of the sources of fintech disruption and could pave the way for startups to expand their relationships with consumers at the expense of banks down the road.

Second, while banking customers say they’re satisfied with mobile banking experiences today, banks need to be prepared to deliver customer service in new ways.

According to Clarabridge, ”only 42% of millennials have placed a customer service call to their bank, which is 25% less than the national average.”

Many millennials prefer to use social channels for customer service, but over a third of customer service requests to banks via social channels go unresolved.

Unless banks update their approaches to customer service, they could find themselves beaten out by online and mobile-focused banks that are better at engaging the next generation of customers.

So while banks may have more time to deal with competition from fintechs than many observers believe, they can’t assume that the apparent satisfaction of their customers with mobile banking experiences makes them immune to broader changes in the marketplace.