Coherence bandwidth/delay spread in OFDM
Indeed, the constraint $T_s(N+N_{cp}) \gg T_m$ should be derived as $T_s(N+N_{cp}) \gg T_s N_{cp} \geq T_m$.

The first inequality to make sure that the CP overhead is as small as possible. The second inquality is what you have said, to avoid ISI between OFDM symbols and to convert linear convolution to circular convolution so that we can use single-tap equalizer.

Thus, $B_N &lt;&lt; B_c$ is a consequence of the prior design criterion. However, if subcarrier spacing $B_N$ is much smaller than coherence bandwidth $B_c$, the channel estimation is facilitated by adding several pilots in $B_c$. For info, in LTE, two pilot are separated by 45 kHz while the rms delay spread is about 1us gives $B_{c,50\%} \approx 200kHz$ and $B_{c,90\%} \approx 20kHz$; thus 45kHz pilot spacing is good compromise between pilot overhead and estimation