Why didn't L check Light's handwriting? Why didn't L check Yagami Light's handwriting and try to match that to the handwriting in the Death Note when he had the notebook?
L had foreseen that the handwriting could be faked. Later in the story, one of Near's subordinates created a fake Death Note containing the names Mikami had written. Mikami didn't notice this since the fake book had "his" writings in it. L, being someone on a greater level than Near, would have thought that Kira might have faked his own handwriting so that just in case the Death Note falls into the SPK's hands, his handwriting won't be used as evidence. Therefore, he didn't even bother trying to check Yagami's handwriting. Also, handwritings are not that distinguishable from one and another. It is very likely for some people to have the same or similar handwriting.

As a side note, we can try to do a similar experiment by showing someone we know our handwriting using our non-dominant hand. I practiced this before and the person didn't notice that it was me writing it, despite knowing my usual handwriting.