It's amazing that 3-4 seconds is considered a reasonable target in 2020 when 8 seconds was a target on freaking dialup. It's like having a Ferrari and considering outrunning a horse a success.
100 ms max on backend processing, 500 ms max on first time to interaction. Client connection speeds matter, obviously. 3-4 seconds is get your fired ass out of here in my world.
That being said, for good UX the target should definitely be under 1 second to interactice, but even on desktop, if your users can't wait 3 seconds after they click the ad, they are not actually interested at all in your product.
People are also used with waiting a bit after they change sites/applications when they initiate the transition, so transition feels faster than it is. It starts feeling slow when you are already on the blank page, having time to look at the loading spinner.
I'm not saying slow is good, but I highly doubt that you can make any site have 500ms TTI for any user (they could easily have 150ms ping to your closest server). I assume that TTI means having access to all website functionality, not some simplified placeholder UI.
And you can doubly tell how much of a PM you are by assuming that everyone is accessing your product by ad and how much you don't care if they are interested after 3-4 seconds. That's a lot of money you're leaving on the table.
Low-end mobile devices are not the right metric for TTI.
Most people don't realize how fast the web can be because they don't bother to benchmark until they are well into the tooling choices and feature development and maybe someone somewhere decides to complain about speed.
A functional Pyramid app with dynamic templates using Mako, and some db queries via SQLAlchemy can fully load in under 100ms.
The bottom line is that speed is a feature. It's not just one feature; it's your most important feature if you want users. It's more important than developer productivity; it's more important than any other feature. You don't know this because you work in a b2b/enterprise space where users don't have a choice. Their managers make the choice. But if you ever work directly on consumer products you'll find this out really quickly. The difference between ~.5 sec TTI and 4 sec TTI is millions of revenue per minute in eCommerce.
But even though it's b2b doesn't mean it has to be bad and suck people's time away from them. You have the option to learn something and change your priorities. But you won't.
I just want to say that I'm not a PM and I don't even work in a corporation. I have worked my entire career focusing on performance (learned programming for and during algorithmic contests were every millisecond really matters, made open-source contributions that vastly improved performance, worked in the gaming space where even users care a lot about performance, and working in the analytics space, where I created a high performance, lightweight alternative to some heavy and data demanding alternatives).
I respect your opinion, but my comment was based on experience, knowledge of human behavior and analytics and A/B tests ran on millions of users. I do agree that it might differ from product to product, but in the majority of cases you just get to a point where it is "fast enough", users no longer notice and spending more time on optimizations takes too much effort for the benefits it brings.
3-4 sec TTI is to be expected from a fully static, server-rendered website delivered from an AWS CF edge through a realistic sloppy mobile connection.
Even at 5+ sec TTI you will probably have green PageSpeed with rating in the nineties if everything else is good.
This may be different for mobile apps.