Wall-modeled large-eddy simulation (WMLES) is widely recognized as a practical approach for simulating wall-bounded turbulence at high Reynolds numbers. Nevertheless, a persistent issue, referred to as logarithmic layer mismatch (LLM), has been observed in both wall-stress models and hybrid RANS/LES models [1-3]. To address this issue, by comparing three different SGS eddy viscosity models, we reveal that ensuring the total-shear-stress-conserved (TSSC) constraint is key to resolving the LLM. Consequently, a TSSC model is proposed and validated in turbulent channel flows at different Reynolds numbers ($Re_\tau = 550, 1000, 2000, 4200$). Our results demonstrate the robust performance of the present model in predicting skin friction and low-order turbulence statistics, even under a relatively low grid resolution ($\Delta_x^+,\Delta_z^+ \lesssim 500, 2 \leq \Delta_x/\Delta_{y,mat} \leq 4$, where $\Delta_{y,mat}$ is the wall-normal grid spacing in the wall-model region). The effect of SGS eddy viscosity fluctuations ($\bar{\nu}_{sgs}^\prime$) is further examined. It is found that $\bar{\nu}_{sgs}^\prime$ plays an important role in predicting the near-wall flow structures when the wall-parallel grid resolution is relatively fine ($\Delta_x^+,\Delta_z^+ \lesssim 50$). Furthermore, the influence of the form and amplitude of $\bar{\nu}_{sgs}^\prime$ is examined, and a `high grid resolution' criterion is proposed to determine when $\bar{\nu}_{sgs}^\prime$ should be incorporated in WMLES. Finally, the ability of the TSSC model (with $\bar{\nu}_{sgs}^\prime$) to capture very-large-scale motions (VLSMs) and inner-outer interactions is assessed. In summary, the mean component of the SGS eddy viscosity ensures the TSSC constraint to avoid the LLM problem, while the fluctuating component improves the prediction of the near-wall flow structures, making the proposed TSSC model robust and effective for high-Reynolds-number simulations.