Some designers include components into every new design just because someone else did once, or because some obscure design rules call for them ...
Anyway, in this particular case, the resistors serve a purpose: It's not current limiting as in DC current, but rather adding some damping to the signals. Fast signal edges can cause signal ringing and ground bouncing, depending on the layout and length of the traces or wires. At some point this leads to interferences or non-working circuits. Putting small valued resistors in series with the signals mitigates this. Usually you'd place them at the signal source (for unidirectional signals).
So in general it's not a bad idea to include them, but most probably you can live well without them and they're not necessary. They're better placed at the debugger end of the programming cable (so most probably they're already included in the ST-Link). Technically, the pin header you've shown above is the debugger end of the cable as this header is intended to debug an external target (if you open some jumpers on the nucleo board).