There are several issues you are dealing with.
Having more domains does not help with search traffic. As a concept, this notion can be thrown away. There is little exception to this rule.
Having sites with little or thin content can never rank. Search engines prefer sites with content. Spam sites have historically hosted thin content, link pages, and generally pages that have no real value. One indication of a site worth listing in the SERPs are sites with significant high value content that enjoys a fair amount of organic links, citations, and good SERP performance. For SERP performance, the number of pages that rank and have a good CTR (click-through rate) is an indication of a sites quality. Sites with little to offer cannot gain SERP performance metrics. Any site with just a few pages will never rank or possibly will never be listed in the SERPs or be dropped over time. It really is about capturing eye-balls- a marketing term similar to butts-in-seats- which indicates your ability to attract users/an audience. Since search engines are about providing quality resources, any under performing site would virtually disappear. Remember that Google is a business and gains at least 10 billion dollars per year just in search alone. It is very easy to erode search results so Google is very wary of any site that does not perform well or they cannot place a good bet on.
Search engines are suspect of spam sites of course.
Linking several thin content domains to a parent company site could easily be seen as gaming. One previous spam tactic was to create lots of domains with little to offer, but were designed to rank well for select terms that linked back to a parent site somewhere. One way to combat this was to simply dismiss any site with thin content. Another was to create relationships between sites and use semantics to determine if gaming was at hand. Even smaller efforts were a problem and so today, smaller efforts will be discovered- if not right away, then after short period of over time. Linking schemes are a real concern and so link patterns are examined within the realm of the related sites and anything suspect would be nipped in the bud quickly and quietly. Since the algorithm(s) for link patterns is/are rather sophisticated, any simple link scheme involving a smaller number of sites would be discovered quickly and dealt with.
Redirection was a common tactic used by spammers- especially in the early days. The most common trick was to register a large number of sites with small amounts of content designed to capture a specific set of keyword traffic then use redirects within the HTML to send the user to another site. This was a HUGE problem! Since at the time search engine spiders did not follow these redirects, these pages were indexed and the spam worked. Today Google knows how to find these types of redirects extremely well and advises strongly against using them. Since it is a legitimate tool for site owners to use, Google will not slap the wrist of everyone using it, however, couple that with several domains with thin content, then it is reasonable that Google will consider this to be one of the worse types of spam there is. Today, Google will not only recognize the code, but wait for the redirect giving a double-whammy detection scenario. This is a strongly inadvisable technique. A redirect of this type from sites with thin content would(!) negatively effect the performance of all the sites significantly and recovery would be slow- likely over a period of years.
Finally, there is the cost factor. While domain name registration and hosting can be seen as small money to some, there would be no return on the cost. For this to work, there would have to be significant content and content is expensive. Each site would have to be an honest one. I have always argued that with little exception multiple sites add no value and that generally speaking, one site would perform better than several. As stated, there are exceptions and generally these are related to topic more than anything else.