Wouldn't it make sense for the heatshild tiles to overlap one another? so that there are no "spaces" between the tiles.

Also, wouldn't that make them more secure as the overlap could be enginered to make the tile's interlocking, thus a single tile would be secured not only by the adhesive applied to it, but also secured by the tiles surrounding it.

One negative of course: How then do you replace a damaged tile?

To relplace a single tile you would almost certainly need to remove and replace the tiles around it.

Maybe a system could be worked out to "chisel" out the damaged tile, and then replace it with a new tile that somehow "snapped" it's interlocking mechanism(s) into place only after the tile was replaced?

Or maybe you just plan on completely replacing the heat shield after each mission? Turn the spacecraft over and hire a few high tech-roofers to remove and then glue in new ceramic shingles after each mission?