Stimulated by recent indications that the binding energy of the hypertriton could be significantly larger than so far assumed, requirements of a more strongly bound $^3_Lambda {rm H}$ state for the hyperon-nucleon interaction and consequences for the binding energies of $A=4,5$ and $7$ hypernuclei are investigated. As basis a $YN$ potential derived at next-to-leading order in chiral effective field theory is employed, Faddeev and Yakubovsky equations are solved to obtain the corresponding $3$- and $4$-body binding energies, respectively, and the Jacobi no-core shell model is used for $^5_Lambda$He and $^7_Lambda$Li. It is found that the spin-singlet $Lambda p$ interaction would have to be much more attractive which can be, however, accommodated within the bounds set by the available $Lambda p$ scattering data. The binding energies of the $^4_Lambda {rm He}$ hypernucleus are predicted to be closer to the empirical values than for $YN$ interactions that produce a more weakly bound $^3_Lambda {rm H}$. The quality of the description of the separation energy and excitation spectrum for $^7_Lambda$Li remains essentially unchanged.
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