LDO vs switching regulator
Switching regulator design is complicated indeed, and it even requires a proper PCB layout thanks to the high frequencies and EMI involved. But it's by no means impossible when building it around a controller IC and following its datasheet's recommendations.

But consider that for about the same 3 euros, you could buy a ready-made switching regulator module on its own little PCB from eBay.

And you don't necessarily even need a switching regulator circuit capable of 2A or more, if those spikes are short enough. You could buck down to let's say 8V and put that into a suitably large capacitor, and further regulate to 5V using a linear regulator. The 2A spikes would make the capacitor voltage dip down, but if it doesn't dip too much (thanks to a big capacitor), the output will remain a steady 5V.