Well, this is the explanation I found in a (different) CDC paper:
First, we based assay designs on previous diagnostic assays that had been developed for detection of MERS-CoV (12) and SARS-CoV (10) and targeted the N gene. Because of the relative abundance of N gene subgenomic mRNA produced during virus replication (13), rRT-PCR assays targeting the N gene of coronaviruses could theoretically achieve enhanced diagnostic sensitivity. One study also showed that the N gene–based rRT-PCR assay was more sensitive than the open reading frame (ORF) 1 assay for detection of SARS-CoV-2 in clinical specimens (14). Second, we designed rRT-PCR assays on the basis of limited genetic information available soon after the emergence of SARS-CoV-2, when it was announced that a novel coronavirus of zoonotic origin was described as being similar to bat-SARS–like CoVs and only 1 SARS-CoV-2 sequence was publicly available. The N3 assay was intentionally designed to universally detect SARS-CoV-2 and other SARS-like sarbecoviruses to ensure detection of SARS-CoV-2 as this virus evolves over time and to improve early identification of future emerging novel coronaviruses from this high-risk subgenus. After completion of this study, the sequence of a new bat-SARS–like CoV, RaTG13 (EPI_SL_402131), was released on GISAID. Detected in 2013 from China, this virus appears to be the nearest bat precursor of SARS-CoV-2 (15), having 96% genome and 97% N gene sequence identity with SARS-CoV-2. All 3 assays are predicted to detect the RaTG13 strain.
So it seems to have been combination of factors of wanting a "universal platform" that could target related viruses as well as the supposed abundance of the N gene making this (CDC) approach more sensitive. However there's no concrete data on comparing it with an alternative approach in this paper. The study "14" (Chu, Pan, Poon et al.) they cite in support is from China/HK. (Also of note regarding the Charite protocol in relation to this, the E gene isn't located in ORF 1, although the RdRp is.)
From a more recent comparison paper (Meijer et al.) of commercial kits--comparison paper which shares authors with the original Charite protocol paper--, tests that use the E gene have some cross-reactivity with SARS-CoV-1, but this is also "by design" in order to target multiple viruses on their platform
In this set-up, the E-gene primer/probe set is specific for bat(-related) betacoronaviruses, and therefore detects both SARS-CoV-1 and -2. In addition, whereas the RdRp-gene primers are also specific for bat(-related) betacoronaviruses, two probes are used: one specific for bat(-related) betacoronaviruses and another specific for SARS-CoV-2.
Interestingly perhaps, none of the tests in this comparison (Meijer et al.) were pure N gene tests, like the CDC one. (There were some that combined an N gene test with another, e.g. one from Spain [ORF1ab, N] and one from Korea [RdRp, N, E]; the RdRp is located in ORF1ab.) Meijer et al.'s selection of kits comes from the broader FIND project, which also doesn't shortlist any pure N tests.