In this work, we have investigated the continuous-wave (cw) lasing potential of thin slab-shaped Cr:LiCAF crystals with a low chromium doping level of around 1% and various lengths of 1 to 2 cm. These relatively long crystals with low Cr-doping facilitate the distribution of heat load in a larger volume and could enable power scaling of Cr:LiCAF lasers. However, long crystals tend to have larger passive losses, and it is also more challenging to achieve efficient mode-matching to the low-brightness pump mode in a longer gain element, which could hinder laser performance. To explore the issue, we have performed detailed cw lasing experiments in single- and multimode diode-pumped Cr:LiCAF laser systems employing crystals with different doping and length. Our results showed that current state-of-the-art crystal growth methods provide Cr:LiCAF crystals with low enough passive losses to enable cw laser efficiencies of up to 50%, even in these long samples. The pump powers available in this study (5.35 W) limited the cw powers we could achieve experimentally to 2.25 W level; however, our simulations indicate that thin slab-type Cr:LiCAF crystals with low Cr-doping have the potential to achieve cw powers above 10 W level.