Here is USPS’s reports on speed https://about.usps.com/what-we-are-doing/service-performance/welcome.htm
If you compare the variance reports for q1 2018 (this quarter last year) to q4, you can see that q1 has much more variance. 2018 q4 also has more variance than the prior year so it seems reasonable that 2019 q1 is not as good as 2018 q1.
From these two pages: https://about.usps.com/what-we-are-doing/service-performance/fy2018-q1-single-piece-first-class-mail-service-variance.html and https://about.usps.com/what-we-are-doing/service-performance/fy2018-q1-presort-first-class-mail-service-variance.html, you can see that for last year 1.1% of mail in the 3-5 day category arrived more than 3 days late and 0.5% of presort first class. The “days” category depends on what zones it was mailed to and from and I would assume the worst case when I have no control over it (bill pay). That’s more than 1 in 100 or 1 in 200 respectively. 1% is not very common, but again it’s plenty common enough to not be surprised if you encounter it. But that’s for the whole quarter. The weeks around black friday are likely the worst weeks of the quarter. The post office makes profit from packages to subsidize the artificially low cost of first class mail. If they don’t prioritize packages in busy times, then they’ll lose that business and everything gets much more expensive.
There are other options that are more reliable or faster, but at higher cost or other requirements (ACH cheaper but needs to be supported on both sides, thus bill pay usually uses ach with known companies they have in their system and only does the mailed check if no ACH possible. Wires are instant but expensive.
For more reliable and trackable mail, USPS has registered mail but it’s not necessarily faster.).
If you’re worried about that, you should look closer at your bill-pay service’s terms. As mentioned up-thread by someone, usually they self-insure to cover late fees if the payment is received later than a certain amount of time after it’s requested. It seem to work out cheaper for the bill-pay service to use the super-low cost budget mailing with low risk of loss or extended delay and pay out any late fees incurred than to pay more for each and every check mailed out. Any delays their actual processor may have had around the holiday are conceivably also weighed against the costs they’re paying out for late fee claims.