3句都可以换为on the top of，但在当代英语的角度看，第一句替换很自然，第2和第3句用on the top of较为罕见，或者这么说，第2，3句在上世纪60年代前用on the top of倒是有见到。

60年代的一本书上面：

“Far out at sea, the water is as blue as the bluest cornflower, and as clear as the clearest crystal. But it is very deep, too deep for any cable to fathom, and if many steeples were piled on the top of one another, they would not reach to the surface of the water. It is down there that the Mermen live.”

还有：

At the end of the street is a school which was hit, and collapsed on the top of 500 people waiting to be evacuated ...

Queen Mother 的 Queen Elizabeth 在 1940年9月13日写给 Queen Mary 的信。2009年她的官方传记出版时，这封信公开。《The Independent》在 2009年9月13日全文刊出了它，而且原文正是：

…a school which was hit, and collapsed on the top of 500 people waiting to be evacuated…

有一本比较新的描述介词的书中是这么说的：

ON THE TOP OF is used in place of ON TOP OF to designate a position on the intrinsic top, as in (c), or simply on a horizontal plane, "on the uppermost or superior part of," as in (d). Notice that, in (a), (b), and (d), the entities are an integral part of their referents:

a) The restaurant is located at the top of the hotel, on the 34th floor.

b) The Ocean-view suites are located at the top of the ship, on decks 16 and 17.

c) There's a spider on the top of the overturned hat.

d) The swimming pool is on the top of the hotel.

…

ON TOP OF is also used in the sense of ON to denote position on a surface (often above or over another surface), or in the sense of "covering a surface," as in:

We placed the sculpture on top of the carpet.

Caravaggio painted David and Goliath on top of a painting by a different artist.

也就是说on the top of X当作 X 的一个可识别的顶部、上表面或最高区域。

而：on top of X除了也能表示“在……顶部”，还已经发展出更宽的关系义，可以表示在表面上方、覆盖在上面、层叠在上面，此外还有抽象的“除此之外、再加上”的意义。

所以这么说，当代英语里，第2，3句不用the是很自然且普遍的用法。