The tiles weren’t so much lost as they were damaged, largely due to debris coming up off the runway during landing. No matter how much NASA cleared and swept the runway, there was always some damage to the tiles. Very frustrating.

Because Starship will not roll along a runway, the problems with their tiles should be different and fewer. Only test flights will tell. Sierra Nevada’s Dream Chaser has already performed a test landing on a runway, but I have not researched whether there was damage to the underside, where their heat shield is or will be.

“But hasn’t SpaceX presented the idea that the Starship will make a very long gliding flight in the atmosphere before landing?”

As I understand it, Starship will not glide like the shuttle but will present the heat shield side into the “wind” like a returning capsule. Starship reenters sideways. The area-to-weight ratio may be sufficient that it slows down more in the upper part of the atmosphere than capsules do, but it does not have lift to keep it high in the atmosphere the way the Shuttle did or that Dream Chaser will. So, it will “fall” sideways until it is slow enough to “fall” more downward.

“They (or Elon Musk) have presented, and scrapped, many ideas.”

If you include more than just Starship then even more ideas have been scrapped. Scott Manley decided to document a few and wound up making three videos, just of SpaceX’s abandoned ideas:
https://www.youtube.com/results?search_query=scott+manley+abandoned+spacex

I think that these tiles are the second or third iteration for the heat shield. SpaceX has been willing to pursue ideas but is also willing to drop them if they don’t pan out well or to change an idea if it takes too long to develop as is. This is why they changed from a composite Starship to a stainless steel Starship.
https://www.youtube.com/watch?v=cIQ36Kt7UVg#t=113 (point is made in the next 30 seconds, but the whole interview is about design and design philosophy)

here we go…
The Graduate
“One Word…”
https://youtu.be/eaCHH5D74Fs?t=25

Columbia was lost due to a punctured reinforced carbon leading edge of the wing, not a damaged or missing tile.

But hasn’t SpaceX presented the idea that the Starship will make a very long gliding flight in the atmosphere before landing? To slowly lose speed and decrease the aerial friction and heat. That’s why it is to have that shark fin wing as a rudder. They (or Elon Musk) have presented, and scrapped, many ideas.

I meant matching in thermal expansion. Depending upon the application, other properties could be desirable to match.

“It is difficult to find matching materials that also perform the other needed functions.”

Why matching materials ?

The problem is similar to the problem NASA had with the Space Shuttle. Large structures flex during flight. It is also why they are using 304L instead of 301 stainless steel. The 304L flexes better.

MDN’s comment about thermal expansion is another important consideration. The heat shield, being hotter than the main structure, undoubtedly will expand more during reentry and the main structure contract more during propellant loading. It is difficult to find matching materials that also perform the other needed functions.

I’m sure that putting the thermal material onto current flight test vehicles is an attempt to avoid big surprises later, as happened with the space shuttle, when they first flew Columbia on their 747 and some dummy tiles fell off. They were not flight installed, however, just taped in place, but NASA got a lot of bad press about it, and people still talk about it to this day.

Wrt the size of the tiles I think many smaller units are likely preferred to accommodate thermal expansion. This way they can leave a small gap between adjacent tiles which would be packed/filled with a flexible thermal material (I believe the shuttle used a thermal rope if memory serves). Starship t’s a BIG structure and re-entry will generate a BIG delta T, so this is something you really need to factor into the design.

If ceramics is needed to make a high velocity landing on Mars, then why not mold the ceramics in a single, or at a least only a few, large segments?