Black's model for interest rate derivatives is a perfectly acceptable starting model for pricing interest rate derivatives in a forward measure using a lognormal distribution assumption with just one time horizon.
The only caveat is that a model that evolves the forward rate curve through time (in order to price more complex derivatives than a cap/floor) needs a drift adjustment to ensure that the model is arbitrage free. How this should be done was not made clear until the later work of Heath, Jarrow and Morton in about 1990. Hence such models, and especially the lognormal forward rate version, are now classified as HJM models.
In the real-world, Black's forward rate model is now only used as a translator to convert cap/floor prices to implied volatility and back. Most dealers price and risk-manage using models which take the interest rate volatility skew into account such as SABR and stochastic/local volatility models.