MTR 7.3 says “Players may use only the cards they receive or draft and basic
land cards provided by the Tournament Organizer.”

I've never seen this rule enforced. I see this rule broken regularly at the
Pro Tour and at Grand Prixs. I break this rule regularly, as I use pre-sleeved
basic lands. I've noticed many judges don't know this rule, because it is never
enforced.

The only time I've ever seen this rule close to being enforced was when a
player had all basic lands that were significantly warped foils, but the judge
only stepped in because the player was playing marked cards, not because they
were using basic lands not provided by the tournament organizer.

Is there any scenario in which I would step in and enforce this rule when there
was not already another problem?

It is not answer for your Q, but as I know of, the rule used to be enforced (literally) in Japan. Don't know if any other place in globe honored it at that time :) However, since last year, we have started to advise player to bring own basic lands to limited events. You may refer following threads for past discussion on this topic.

http://apps.magicjudges.org/forum/post/62668/
http://apps.magicjudges.org/forum/post/71494/

As far as I know, it serves two purposes:
1. Making it clear that TOs need to provide basic lands for players.
2. Giving us something to fall back on in case there's a problem with basic
land provided by the player or someone other than the TO.

Really, it's more this: “Giving us something to fall back on in case there's a problem” than this: “Making it clear that TOs need to provide basic lands”.

Given that basic lands aren't as plentiful or available as they once were, it's fine to allow players to use their own (*unmarked*) lands.

d:^D

I always alert a judge/the head judge at any limited events that I have my own land. I then let them inspect the land and box/container that they're in, so there are no chances for confusion or me slipping in a legal card/cheating.

When I judge such an event, I announce that if someone has their own lands, to let me check them.

I do the same thing as Jeremy when I play. My “Limited Box” has 30 of each basic and 50 sleeves, and to date, I've never had an issue with being allowed to use it.

As a note, there are some shops that take a very strict interpretation of this. At one of the shops in my area the TO has a blanket “you may not use your own lands” policy for limited events. Their argument is that the MTR requires people to use store lands.

Personally I'd like to see the MTR changed to have less definite language here. Something along the lines of:

“Players may use only the cards they receive or draft and basic land cards provided by the Tournament Organizer or approved by the Head Judge.”

Or just:

”Players may use only the cards they receive or draft and basic land cards approved by the Head Judge.”

Got there in the last MTR update. :) “Players may use their own basic lands during tournaments.”