If you have some type of horizontal or track dropouts on the bike, there is no reason for a chain tensioner. Just cut the chain to length, then pull the chain tight by moving the wheel.

Half links are available for some chains to make it easier to use short dropouts, or to give you a bit more adjustment.

If you have vertical dropouts, then it is much more difficult to ensure perfect chain tension.

Also keep in mind that as chains wear, they will stretch slightly. So, if your tension is perfect now, put 5000 miles on the chain, and the tension will be off.