"I got an exclamation mark when I tried the first formula you suggested.
"
Do you mean an exclamation point in a red triangle? That's an Error triangle. Clicking it once will open the error message (created here deliberately).

If this is the message you got, the likely cause is that your region uses the comma ( , ) as the decimal separator. If that's the case, replace the comma in my formula with a semi-colon ( ; ).
Otherwise, check that the formula exactly matches the one shown below. ("include-headers" is entered as a zero ( 0 ), but displays in the editor as shown)
Here's the formula as it appears in the Formula Editor for my test table. The result is displayed in the selected cell.

The result is a count of all the columns in the table. The maximum value (shown) is the limit to the numbers of columns allowed in a Numbers table.
"When you say "column reference tabs" I'm assuming you mean the letters that label the columns. They are seemingly endless. After "Z", it starts on "AA, AB, AC..." and at the end of that it goes on to "BA, BB, BC...", etc.
Correct. The reference tabs appear only when at least one cell is selected in the table.
The largest possible tab label is IU, equivalent to 255.
"I've tried selecting multiple columns and deleting them, but they reappear again."
As noted above by Badunit, they are not "reappearing." When you delete columns C, D, E and F from a table containing at least four more columns (G, H, I and J) to the right of these, those columns shift leftward and their labels shift four places toward the font of the alphabet. G becomes C, H becomes D, I becomes E and J becomes F. And so on.
"They are seemingly endless"
'Seemingly,' but they will end, somewhere before you reach column IV.
To get to the last column quickly, click on the bottom cell of the first empty column, then press command-right arrow.
Regards,
Barry