Do pilot uniforms always include a shirt with stripes?
Uniforms are to make it easy to identify members of a group who have a separate function or authority from a larger more random group.  The stripes are to easy to identify the chain of command within this group at a glance.

Most of the time it's all just costume peagentry.  

When the shmoozle hits the fan however, being able to identify who's in charge and next in charge and so on, without having to, you know, ask around, becomes a big deal.  That's why the bars.

You won't find a first or second tier carrier in a Western airline without a uniform shirt and rank bars.  I can't find any specific regulations that require that, but it's basically an old convention carried over from the marine world (it's why pilot uniform suits look like naval uniforms), where many of aviation's traditions originate.