That doesn't look like a standard pot, though maybe that depends on what you consider standard. 'Standard' pots have an edge along the lower rim, and enough holes in the bottom that I have never seen water pool at the bottom like that.
That being said, I don't think it is a huge problem. Most ends up getting used up quickly or drains away more slowly. I'll often leave a bit of water in the saucers in the summer to try to lengthen the time between waterings, also to no ill effect (my plants are all in straight bark).
If it is a problem for you, I would consider switching to better pots or adding a layer of inert material at the bottm rather than spending time with towels/paper towels getting the excess water out. Watering plants takes enough time as it is!
For reference, this is what I consider 'standard' :
10cm clear plastic pot or this with air cone :
12cm clear plastic pot