Fair point but…
Not to get too far side tracked from the main thread but…
Although you say the green “can’t support the niche they fill in degraded habitats” (paraphrased) which is partially incorrect, they can, and do still exist in urban environments, they are just more likely to be predated. Without the introduction of brown anoles, there would simply be less green anoles at first and then with time an increase in less green morphs. The increase in less green morphs in urban areas is still seen even with the introduction of cuban anoles.
One of the trends of invasive species is “specific traits that allow them to out-compete native species” So going on the original question of the thread, it was asking about non-invasive introduced species and cuban anoles are considered be an invasive introduced species.
https://www.cabidigitallibrary.org/doi/pdf/10.1079/cabicompendium.107830
“The successful occupation of different types of habitats by Norops sagrei (brown anole) is attributed partly to its use of thermo-regulatory behaviours such as basking in solar radiation to select acceptable microclimates at different latitudes and altitudes(Rogowitz,1996). It is reported that brown anole when present, reduce the density and diversity of spiders upon which they feed (Wardle, 2002). Greeneet al. (2002) state that, brown anole competes successfully with native green anole (see Anolis carolinensisinIUCN Red List of Threatened Species) and other introduced congeners. Campbell (2002) observes that without the brown anole,the native green anole occupies perches from ground to crown, but the presence of the brown anole causes the green anole to move higher, occupying trunks and crowns of trees. Brown anole demonstrate intra-guild predation (IGP), which is defined as killing and eating among potential competitors and have been reported to prey on the hatchlings of green anole… (Nicholson et al. 2000).”
“Anolis sagrei may have negative impacts on native herpetofauna. For example, it has been implicated in declines of the North American green anole (A. carolinensis) in southeastern USA (Campbell, 2000) by predation (Campbell and Gerber, 1996; Gerber and Echternacht, 2000), interspecific mating (Sater and Smith, 2018) and competition (Losos et al., 1993; Culbertson and Herrmann, 2019), with induced habitat shifts and decreases in population density (Campbell and Echternacht, 2003). Experimental introductions of A. sagrei showed that it increased dramatically in density at the expense of native A. carolinensis (Campbell and Echternacht, 2003). Furthermore, asymmetrical intraguild predation exists between introduced A. sagrei and native A. carolinensis from Florida and A. conspersus from Grand Cayman (Gerber and Echternacht, 2000). However, scientific studies have shown, or suggested, declines of green anoles where brown anoles are present; though none concluded that brown anoles caused the local extinction of green anoles (Campbell, 2000; Cassani et al., 2015). Furthermore, the recent establishment of A. sagrei in Bermuda has been identified as a potential threat to the survival of the critically endangered Bermuda skink, Plestiodon longirostris (Stroud et al. 2017), but no further evidence is available. It is observed that the Miami blue butterfly (Cyclargus thomasi bethunebakeri), listed as endangered under the US ESA 1973 (as amended), was preyed upon by an adult brown anole lizard (USFWS, 2012)”
I would still say it is not an overall benefit and at least neutral in certain environments. Like some other examples in this thread you are only considering them to benefit the ecosystem because of initial human disturbance. It is complicated since the decline of green anoles is partly due to urbanization but also because a new species is better adapted for the new urban environment. As studies show the out-competing of brown over green extends beyond urban environments.
But as Non-native species dominate herpetofaunal community patterns in both native and non-native habitat patches in urban Miami-Dade County shows one of their conclusions “our study did not find evidence of a direct negative impact of non-native abundance on native abundance. Instead, we found a positive correlation between native and non-native herpeto-fauna abundance” but that was a more general study on herps not focused on just anoles.