What is "good" exactly? What is "lawful"? It's nice to have D&D deal with morality, but quite frankly WOTC(and everyone else I've seen) sucks at defining it. They either create something so vague or wishy-washy as it's impossible to actually nail down in an effort not to offend people, or they create something so specific that it prevents a player from thinking creatively.
The latter is generally the problem with the LG paladin...hell the alignment restricted ANYTHING. Alignment is often so narrowly defined as it generates what was termed "lawful stupid", where a player isn't actually lawful good, but are so terrified of losing 99% of their class features because actually doing good could be outside the law. That's the paradox of "lawful good", because really, lets look at many "good" historical figures. Ghandi. MLK JR. Rosa Parks. etc...
These people are generally considered champions of "good" and even fair laws, but all of them had to break existing laws in order to achieve their goals.
How do we differentiate between a "good" law that should be followed, and a "bad" law that shouldn't? The DM plays both the PC's god, and sets the social norms of the society the party is in. This is a clear conflict of interest. Obviously if LG Paladin Bob is in the LE Kingdom, then there are pretty much guaranteed to be laws and morals and social systems that are utterly repulsive to the concept of "good". But it is still a lawful kingdom, even if it's nature is evil. How does bob reconcile this? Does he follow the laws, thus being "lawful stupid", ie: the law is the law, no exceptions, and therefore not do good things? Or does he do good things, even if they are in violation of the law? Who determines if Bob is being lawful? Who determines if Bob is being good? I'll tell you who it's not: It's not Bob! It's Bob's DM.
Which is the ENTIRE problem. Bob is required to follow an alignment code that he gets NO SAY in. He doesn't get to decide between a good deed and a lawful one, the DM decides if his deed was good or lawful. So Bob stops thinking. Bob falls back into "lawful stupid", where Bob does whatever the DM says will allow him to keep his powers.
I LOVE that 4e eliminated this. 4e was the first edition that I could honest-to-goodness play a Paladin who was both lawful AND good. Because my Paladin could follow a code that I derived from the domains of my deity, not a code set down by my DM. My paladin believed in a fair rule of law, that bad laws should be broken, ignored, and overturned. My paladin believed in doing good, by smiting the wicked but not doing so out of anger or vengeance, but out of a desire to protect others. It was the best paladin I ever played because I actually got to play it!
So this is the problem with alignment restrictions, in short they either:
A: are meaningless because they're too ill-defined to matter.
B: force players to stop thinking because they're so narrow and their punishment so extreme as they make players not want to take the risk.
And that's not even getting into the subject of polarized DMs or those who actively try to challenge a party morally.
The powers of a Paladin are not even in the eensey-weensey, tiniest way cool or powerful enough to warrant the kind of BS that alignment restrictions cause. In any game where the DM has even a vague inkling of moral leanings, you're better off just playing an honorable fighter...who honestly will play much better and never even have to blink an eye at alignment restrictions, even if that fighter is lawful to a fault and good through and through, a LG Paladin gains nothing of value from their alignment compared to other classes, while they lose everything if they aren't.
That isn't fun. That's stupid.
