A common belief in designing deep autoencoders (AEs), a type of unsupervised neural network, is that a bottleneck is required to prevent learning the identity function. Learning the identity function renders the AEs useless for anomaly detection. In this work, we challenge this limiting belief and investigate the value of non-bottlenecked AEs. The bottleneck can be removed in two ways: (1) overparameterising the latent layer, and (2) introducing skip connections. However, limited works have reported on the use of one of the ways. For the first time, we carry out extensive experiments covering various combinations of bottleneck removal schemes, types of AEs and datasets. In addition, we propose the infinitely-wide AEs as an extreme example of non-bottlenecked AEs. Their improvement over the baseline implies learning the identity function is not trivial as previously assumed. Moreover, we find that non-bottlenecked architectures (highest AUROC=0.857) can outperform their bottlenecked counterparts (highest AUROC=0.696) on the popular task of CIFAR (inliers) vs SVHN (anomalies), among other tasks, shedding light on the potential of developing non-bottlenecked AEs for improving anomaly detection.