It seems very likely that the quality of news gathering would diminish if newspapers were no longer in existence. TV news has a very difficult time being as serious as newspapers are and internet media at this point depend strongly on newspapers.
If newspapers disappeared, a major source of news would be TV, just as it is now. The trouble with TV news is that it is as much entertainment as it is news in many cases. TV news programs are less likely to cover complicated stories and less likely to cover stories in depth. News would become more superficial if newspapers were to die out.
If newspapers disappeared, the main source of written news would be internet sites. The problem is that most internet sites that provide news today are not involved in reporting. They comment on and link to content provided by newspapers, but they do not report much. The bulk of content is provided by newspapers and their employees. If newspapers cease to exist, there would be no sources for such sites to use.
Thus, it seems clear that the death of newspapers would significantly damage the quality of newsgathering.