The minimum tax for the Assumed Par Value Capital Method of calculation is $350.
you save $175/year and any time you wish or for example receive external investment you can do a stock split or authorise more shares.
For example, amending the certificate of incorporation to authorize more shares is probably going to cost around $500 a minimum (and definitely much more if you use a lawyer). That's roughly triple the $175 in tax savings you get from authorizing 5,000. But of course by then, you probably would have already issued shares to people, so you would probably want to do a stock split. That's going to definitely require a lawyer... my guess is at least a few thousand in legal fees.
So it seems like it could make sense if (1) you don't plan to ever raise venture capital or (2) you think it'll be at least 3 years or so before you raise venture capital and you can hold off on issuing stock until then (unlikely to be a good idea). I suppose the analysis would also be affected by the time value of the $175 / year. E.g. how much more that $175 means to your company now than it will a few years down the line.
though i do agree, some of these small savings may or may not make sense depending on what you want to do in the future.
But in any event, I was referring to authorizing more shares under the certificate of incorporation - which is basically setting the maximum number of shares that the company can issue. That's a different process than issuing shares (though every time you issue shares, you should make sure you have enough authorized and available for issuance).