there’s an interesting (more radical) suggestion in this metrologia paper to make the second more like the other new SI units

“fixing the numerical value of one more fundamental constant, in addition to c, h and e. From the fundamental standpoint, a good choice for this constant is the electron mass m_e, in which case the system of units is set by the relations:

m_e = M kg,

where M is the defining value, completed by the other defining relations for c, h, e, k_B, N_A and K_cd.”