The authors should do a comparison with recent work on HE for inference on other model types. Logistic regression is a subset of neural network inference, and there is significant prior work that appears to be competitive with their results.
Recent work [0] shows that MNIST, for example, can be done in a model secure/data secure way with online 30ms inference latency. For ~500,000 samples, evaluated sequentially, that's roughly 5 hours, which beats their time by about 3x. Perhaps I'm missing details in my read of the paper.
[0] Gazelle: A Low Latency Framework for Secure Neural Network Inference https://arxiv.org/abs/1801.05507