I do understand that concern, which was my biggest issue with the 'small Lamps' idea the Hosts have come up with. And, in a world untrammeled by the laws of the universe, why not just make them impossibly big?
I do think we have some 'ratio' issues to deal with, though. The Eiffel Tower is a good way to show 'wide base supporting a pillar' in a seamless arrangement that we seem to prefer.
If we make the Lamps 325 miles tall (not the tallest suggestion in this thread), the mountain base will need to be 125 miles in diameter. That...is a freaking big mountain, and it's for all intents and purposes unmovable. Sure, you can break the pillar and knock down the Lamp, and you can have molten light/stone burning up the forests for miles around....but that base isn't going anywhere. So....what happens to these two giant mountain bases after the destruction of the Lamps? They...should still be there, and continue to dominate the geography of Arda throughout all the coming ages. But....they will not. How long do you think it's going to take to wear the Himalayas down to look like the Appalachians? And then keep in mind that these are 65x taller than the tallest of the Himalayan mountains - we're talking about a really, really, really, REALLY big pile of rock. That's like taking the northwest corner of Mordor, from the Black Gate down to Minas Morgul, and making the entire Plateau of Gorgoroth one impossibly big mountain.
If we want to keep the height but lose the massive mountain base, we change the outline, and that is where we wind up with something a bit unbelievable - a soaring spike jutting out of a mountain too small to anchor it in place. We likely have some wiggle room (we don't want the pillars to actually look like the Eiffel Tower!), but keeping some proportionality is important for keeping this 'realistic' (even if it is impossibly big).
I remember that when we discussed the episode where the Lamps were constructed, Ouzaru brought up the point that Olympus Mons is so massive it is breaking the crust of Mars. It's 16 miles high; can we really get away with a mountain that's more than 60 miles high?