You are not supposed to. The upstream device is sized for a maximum current and daisy chaining can lead to a scenario where downstream devices are sized for larger current than upstream devices, which is avoided everywhere else in electrical distribution.
So it's fine as long as you control the strip and keep track of loads (e.g. you know your spouse will never plug a vacuum into that handy receptacle you have there), but at work your EHS team will mark you down for it.
Daisy chaining is irrelevant to the problem that you can buy 18ga "lighting-only" extensions that bear a 15A rated NEMA 15R but are limited to 8A.
Daisy chaining a power bar with it's own circuit breaker can be ideal if it prevents someone from making the mistake of using a circuit in a way that trips a panel breaker, ie preventing your spouse from plugging a vacuum into a circuit shared by several rooms.
In the UK, if I have a 6 way strip sized for 10A, which thus has a 10A plug in, I could then plug in a 4 way strip downstream with a 5A fuse, then a lamp with a 3A fuse, and that's fine. I could even connect it the other way.
If I plug in a heater pulling 10A then sure, the 5A fuse will blow.
Daisy chaining multiways will increase the resistance in the earth wire which could mean you end up with a class 1 device with a fault connecting live to earth which would only punting say 8A to earth due to a high resistance (but then your circuit's RCD would trip with that), but is it a major problem?
With the US system, do you not have wires capable of 3A (say 24 AWG) which you can connect to a normal socket which also takes a 10A vacuum?
If that lamp has a fault where it pulls 6A, what protects the 3A wire -- i.e. there's a fault with your lamp which is plugged into a 15A circuit breaker, and the lamp draws 10A, it wouldn't trip the breaker, and that nice thin 3A lamp cord would melt.
There is protection, just not at the cable itself.
UK only needed to introduce that because of their ring main architecture, which was fused at levels above a plug.
Also c.f. extension coils and pre-battery vacuums: both needed their cable full unspooled to reach their full load rating.
Yet they typically lack technical enforcement mechanism to not rely on users being literate and willing enough to RTFM.
Safety margins in what you call a 3A cable. And each circuit being fused at a lower 16A, not the 30A that my British house had.
Something like 1.5 mm2 (only a 0.5mm diameter) is able to handle 12A if the insulation survives heating up to 60 degrees and 18A if 70 degrees is acceptable. The whole circuit would have a 16A fuse at the fusebox, so you're not going to get to 70 degrees.
Far from ideal, but also very very unlikely. Because a short would be over 16A and blow the fuse. So we're talking about some situation that's far from a normal load (any device that's close to such a load would need a different cable to be certified), while still remaining right under the maximum load of the fuse that's covering the circuit.
Homes aren't burning down all over the rest of Europe all the time, while fuses in plugs aren't a thing here.
It’s less about being happy about it, and more about ignorance, industry/legal inertia, and the complete lack of me being the global benevolent dictator for life. Sure some might initially resist my efforts, but they’d come around after receiving an appropriate reeducation at my fire safety camps.
In your example there's a first undersized UPS A, then another UPS B, then whatever combination of electrical devices which power usage exceeds UPS A. You say this is problem.
If you have said combination of electrical devices, and if you're assuming we're using an undersized UPS A + the combo of devices, why does the UPS B matter?
If you're going to overload the UPS A you're going to overload the UPS A regardless of UPS B, no? Daisy chaining or not, that doesn't seem like the actual problem to a knee-jerk thinking.
So it's fine as long as you control the strip and keep track of loads (e.g. you know your spouse will never plug a vacuum into that handy receptacle you have there), but at work your EHS team will mark you down for it.