Two points:
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if you look at those datasheets for the devices, many of them will go down to 2-ish volt or even 1-ish volt for newer devices. So they don't have to work at 5v. The arduino happens to be designed to work with 5v. But if you were to jump that regulator, you can go down much lower than 5v. BTW, they don't need that 5v to be precise either.
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even in a non-LDO regulator, the minimum voltage drop over the regulator is substantially lower than 1.4v at low current levels. The LM317, for example, has two p-n junction on the output path. So it needs 1.3 - 1.4v to deliver full regulation at its rated current (0.5 - 1.5a). However, your mcu will drow substantially less than that - on the tune of 20ma on a good day. So the required voltage drop will be substantially less than 1.4v.