The idea behind Simplification was not really to write faster - it was one of several other movements to abandon the administrations and culture of Imperial China, and modernise into the Republican Era. One of the other movements to do with language completely succeeded, which is why the common Chinese language is now based on a vernacular standard rather than literary Chinese.
The premise that the script was preventing China from modernising is an unfounded one, of course, which is why all Simplification movements have actually failed. Mainland China's script reform is permanently stuck in limbo, and Japan's script reform is currently in reverse trend. As late as 1980, the Republic of China (Taiwan) government tried to introduce 行書 as the official script with the publication of 《標準行書範本》, and it also failed.
Simplification, at least in its original inception, has little to do with writing faster. It was one of the many ideas from revolutionary intellectuals at the end of the Qing dynasty wanting to get rid of the shackles of Imperial China and thrust the country into a modern, Republican form of governance. Drawing direct inspiration from "advanced" 1900s European powers, characters were blamed as a blockade to literacy/education. To quote a few typical opinions at that time:
(If) Chinese characters are not abolished, China will surely perish.
Chinese characters are of an extremely uncivilised origin; their shapes are extremely unnatural, learning them is extremely inconvenient, and using them is extremely inefficient. They are truly cumbersome and crude, are the symbols of snake-gods and ox-demons, and are the world's most inconvenient tools.
Key members of both Nationalist and Communist China, including Chiang Kai-shek and Mao Zedong, were extremely zealous of these ideas right up till their death.
-- 人民日報 1977年12月20日
-- 中華民國陸軍一級上將 何應欽《整理簡筆字提案的回顧與前瞻・引言》
Their attempts at implementing Simplification were met with either apathy or resistance at every step of the way. The illiterate masses couldn't have cared less, and were more concerned about putting food on the table for the next day, while contemporary evidence that script had nothing to do with the country's development could easily be found if one looked east towards Japan, which rapidly modernised whilst keeping Traditional Characters.
The Simplification movements were an intermediate step towards the goal of a full conversion to an alphabet script, but Simplification was quickly abandoned after widespread education and promotion of literacy among the general population:
- Republic of China's Simplification attempts were dealt a fatal blow by 1936;
- People's Republic of China's Simplification attempts waned after its first implementation, and completely died after 1978 (see Second round of simplified Chinese characters);
- Japan's Simplification attempts have been steadily reversing. The number of permitted official characters is constantly increasing, and Simplified component shapes are no longer applied to re-incorporated characters.
- 1946: 1,850 characters
- 1981: 1,945 characters
- 2010: 2,136 characters
I assume that all these native Chinese people in favour of simplification were infinitely better educated than I am.
This is not a very good assumption - your average native speaker doesn't qualify for anything apart from letting you know what sounds correct in contemporary Chinese. Any opinion about the Chinese script that's not from professionally trained linguists and/or paleographers should be taken with a grain of salt.
To give an example, there's a widespread but frankly ridiculous idea among native Chinese speakers that "characters have naturally Simplified over time", usually used in defence of the Mainland Government's implementation of Round 1 Simplified Chinese. Apart from most of them cringing at the idea of changing the script to Round 2, the idea completely fails both in theory and practice:
Hypothesis: characters naturally simplified over time. By extrapolation, this means that Chinese ancestors must have written a script that's unfathomably complex.
Sorry, I don't see it. It looks like characters increased in complexity until the Warring States to Qin period (images 3-4), and stopped changing in complexity after that.
Hypothesis: the common folk created vulgar variants (俗字) by cutting strokes off characters, because the official characters were too difficult to write. By extrapolation, the vast majority of variant, non-official characters should have less strokes than the official characters.
I seriously suggest having a browse through a proper collation of vulgar and variant characters. Here's「雨」and the number of vulgar "simplifications" that people invented over the years for it because "it was too difficult to write".
The people did not simplify characters! They changed characters to suit their needs to clarify or enhance their utility in expressing their language, both by simplifying and adding strokes. Pure Simplification is an artificial policy pursued by the Republican governments.