Why is Tom toothless in Harry Potter?

Magic doesn't seem to be able to reverse the effects of ordinary ageing. Noting that Tom has been the barman since the late 1930s, which means that he must be at least into his 80s at the time of the first novel, if not older.

A little man in a top hat was talking to the old barman, who was quite bald and looked like a gummy walnut.

It's likely that Tom lost his teeth simply as a result of poor tooth hygiene and normal senescence. You might want to note that there's at least one other wizard missing his teeth, an equally elderly Grindlewald.

At once, Harry’s scar felt as though it had split open again. His true surroundings vanished: he was Voldemort, and the skeletal wizard before him [Grindlewald] was laughing toothlessly at him.

_{^{Harry Potter and the Deathly Hallows}}

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Other examples of non-reversible ageing include elderly Amos Diggory using a wheelchair in Cursed Child.

And older Albus Dumbledore wearing glasses.

Because we are not shown that teeth can be regrown.

Hermione did not lose her teeth she was struck with a Densaugeo spell and...

It wasn't a pretty sight. Hermione's front teeth — already larger than average — were now growing at an alarming rate; she was looking more and more like a beaver as they elongated, past her bottom lip, towards her chin — panic-stricken, she felt them, and let out a terrified cry.

_{Harry Potter and the Goblet of Fire}

When Madam Pomfrey was shrinking her teeth back down, Hermione simply allowed to be shrunk further than their previous actual size.

Well... when I went up to Madam Pomfrey to get them shrunk, she held up a mirror and told me to stop her when they were back to how they normally were," she said. "And I just... let her carry on a bit." She smiled even more widely. "Mum and Dad won't be too pleased. I've been trying to persuade them to let me shrink them for ages, but they wanted me to carry on with my braces. (ibid)

One can assume that once Tom actually lost his teeth, for whatever reason, they could not be grown back.

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A little real science that may explain why we see bone regrowing (i.e. Skele-Gro) and not teeth.

The exterior of bones consists of periosteum, a dense, smooth, slippery membrane that lines the outer surface of most bones , except at the joints of long bones, which instead consist of slimy hyaline cartilage. Periosteum contains osteoblasts, or cells that can manufacture new bone growth and repair.

Tooth enamel, unfortunately, doesn't have the same regenerative powers. Unlike bones, teeth cannot heal themselves or grow back together if they are broken. When a bone fractures , new bone cells rush in to fill the gap and repair the break, but a cracked or a broken tooth can require a root canal or even total extraction.

_{Why Are Teeth Not Considered Bones? By Remy Melina March 18, 2011}

In my theory Skele-Gro may simply activate and accelerate the process of the bone cells and osteoblasts.

There could be plenty of reasons for this-

1. Difficulty - Not everyone could be so talented as to grow back teeth from nothing. You can't just grow teeth from nothing. Even if it is possible it has to be very delicate work requiring professional skills.

To be a healer you need N.E.W.T.s of at least grade 'Exceeds Expectations' in the subjects of Transfiguration, Potions, Charms, Herbology and Defence Against the Dark Arts, which isn't an easy thing to do.

This brings us to my second point.

2. Cost - It surely would cost a lot considering it takes professionals to do it. Just because there is magic doesn't mean everything is possible. And Tom is never shown as a rich guy.

3. Just why?- A lot of people even in real life are toothless or have a very fixable oral problem. They just don't see the fuss about this harmless problem, nor do they care. Come on, he runs a very busy hotel, he can't just waste a day at St Mungo's.

The example you are referring to is a fairly uncomplicated matter requiring a simple shrinking spell, while Tom's case is different.