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Power supply units are often large relative to the outlet and block access to adjacent outlets in a power bar.

A simple solution is to use 1/2 ft or 1 ft (15cm, 30cm) power extension cords to keep all outlets in a power bar available.

Yet my hunch tells me that doing so increases the fire risk.

Could someone with actual knowledge in the matter pitch in with an opinion?

Does unblocking power bar outlets through short extension cords increase fire risk?

I am not considering an exotic setup (daisy chaining, forking, etc..), nor will the wattage be high (laptop and paraphernalia, at most a stereo amplifier in one slot). The question is whether this increases the risk of fire. The idea is that there are now many more places where rust, or just a poor contact, will happen. And rust/poor contacts cause heat that can spiral to something sinister.

Update

I marked Isherwood's answer right, but thanks to Harper's and Owain's answers I see now that there is an abundance of options to avoid even a small increase in risk. One key keyword is "metal". Search, for example, for "metal power strip" to see ones where right angle plugs will not occlude adjacent outlets. Some have a larger inter-outlet spacing. The challenge is find one not painted yellow.

Yes, but negligibly.

Any connection increases fire risk by increasing the chance of heat buildup due to resistance, sparks due to arcing, etc. The question is how much, and the answer is not much.

Since you already probably have dozens of such connections in your home (including such high-current things as a microwave and kitchen range), and since most of these are low-current devices, I see no reason to be concerned.

One caveat would be the potential for heat buildup around the transformers. They're normally held captive by wall outlets or power bars and not likely to end up in a heap on the carpet. In combination, many transformers without good cooling airflow could overheat. Don't let that situation arise.

Make sure all hardware is in good working order and be happy.

In fact, there are UL-listed power strips that provide an octopus of short cords-on-sockets. (by the way it was hell to find a genuine UL-listed unit of good provenance from Stanley; most of the Amazon listings are cheap Cheese junk off the Amazon marketplace.)

It depends

If it's blocky because it's a wall-wart style transformer, then normal loads simply won't allow it to get warm enough. Wire/adapter/bad connection heat is a function of appliance power squared, so a 1000 watt air conditioner makes 10,000 times the wiring heat as a 10-watt power block. That's how it's possible to sell the total junk often seen on BigClive etc.

However, if it's blocky for some other reason, like an in-cord GFCI for a heavy draw appliance like an air conditioner or hair dryer, that's a no-go. Don't even connect such a load to a power strip in the first place - it should only go either a) direct into the receptacle, or b) straight from the receptacle to the appliance via a 1-socket heavy 12 AWG appliance-grade extension cord.

Quick test question: Which draws more power: a 75 pound, 10,000 BTU wall air conditioner? Or a common hair dryer?

The air conditioner is typically 800 to 1200 watts. The hair dryer, like most cheap resistive-heat appliances, is almost always 1500W or more. Both are too large for power strips. Point being, a "high power" appliance isn't necessarily obvious. A good measure, though, is they make a fair bit of heat.

The problems of 'greedy' power supplies can be resolved by using power bars which have proper individual sockets for each position. They also tend to have better quality contacts than the cheap multi-way strips.

from

https://olsondirect.co.uk/oldsite/13a_standard_flat.htm

They also do USA standard ones, eg

https://olsondirect.co.uk/oldsite/usa_15amp.htm

An alternative solution for your photograph is to use a single larger+higher capacity PSU and connect the low power devices directly. A lab power supply would be ideal and can be set to a variety of voltages, but generally only one, maybe two voltages, so don't connect 5V and 12V things to the same line.

They're expensive, so a DIY solution is to convert an ATX PSU from a computer to a bench power supply. Example:
and an index of projects at https://www.instructables.com/id/Encyclopedia-of-ATX-to-Bench-Power-Supply-Conversi/

You could simply replace multiple USB chargers with a single USB power supply, like this 10 port charger:

capable of 9 devices at a time plus a QC port to charge a laptop at 60W, or something smaller like :

capable of 4 devices at a time.

As other answers state, the extensions shouldn't add any significant fire risk.

For that to be true, however, each extension cord should be rated for (at least) the maximum current allowed by the upstream breaker! (or the power strip's breaker, if it has one).

A standard, lower-price extension cord may be #16AWG, which is rated for 10A. Your wall outlet is likely rated for 15A (in the USA, at least).

If you went with the 10A cords, and an end device draws 15A, the cord could melt and catch fire without the breaker being tripped. This may happen because of an electrical fault, or because you plugged in a higher-power device.

So, ideally, you should check your breaker. If it is 15A, go with #14AWG extension cords. If it is 20A, choose #12AWG cords. Short #12AWG cords may be hard to find, and expensive :)