Why is there no singular form for the tongs?

There is a singular and plural form for the noun tongs. The Word tongs is actually a shortened form for 'a pair of tongs' (singular), or pairs of tongs (plural). Examples of other shortened forms for 'a pair of' are:

• a pair of binoculars, two pairs of binoculars
• a pair of glasses, two pairs of glasses
• a pair of pajamas, two pairs of pajamas
• a pair of pants, two pairs of pants
• a pair of scissors, two pairs of scissors
• a pair of shorts, two pairs of shorts
• a pair of tweezers, two pairs of tweezers

The part of the term is used alone (tongs) because the rest of the term is understood. This form of singular and plural only applies to things that are made by joining two parts to make a single object. For example you can separate a pair of shoes or a pair of socks and you will still have a usable shoe or sock; but if you separate a pair of tongs, or pants, or scissors, they're not of much use.