I remove them if I'm nearby, but I don't worry about them otherwise;
they'll eventually fall off.

& I put 'em back into the soil, either in the garden to deteriorate in place or in the compost pile.

In most cases it is up to you to determine the 'look' you wish to have. Some would find a plant with some dead leaves unsightly, others couldn't care any less.

If the plant has a disease such as a fungal problem then always remove the dead leaves, but in the absence of disease it is generally fine to leave dead leaves on health wise.

Dead leaves should not be plucked from plants. Better, is to cut through the petiole (stem) with a scissors or defoliating tool. Pulling leaves injures/breaks small branches and can break fine roots on small & marginally established plants. The main reason, though, is it damages axillary buds as the petiole is torn free from the branch. Axillary buds are the little buds in the crotch of each leaf that are waiting to be activated when the leaf dies or is badly damaged or removed.

Al