Personally I like dotted lines. It's more than 40 years since last I had a job where there weren't any, and I suspect that most people work with more dotted lines than solid ones.

A very long time ago I had formal management training in what was called "matrix management" - that was the management structure of an organisation where many of the dotted lines were formally recognised and institutionalised (but they certainly were not solid lines) - and that made it easier for me to understand that I must go outside the line management structure for advice/assistance/guidance and not always rely on my line manager, and that the same applied to people reporting to me - they needed the freedom to get guidance from other senior people; and equally I needed to provide advice and guidance to people not working for me. I would hate to go back to work in a strictly hierarchical system now.

I've had line management jobs, non-line roles where I've had a very small team to assist me in helping the line managers, and non-line roles where I've had no direct reports; often in the non-line roles my line manager hasn't had a clue what I'm doing but could see the results (if a non-line senior manager in some unit is always calling people to come and see him there's something wrong; if he's overwhelmed by the number of people coming to see him or telling their managers to get his views before taking a decision h'e probably doing a good job; but the bottom line is "is the unit for which he provides that function successful").

I've see the dotted lines go wrong - where people somewhere in the matrix didn't fully understand their roles and responsabilities. Only twice in my career have I seen this happen (once when a senior line manager wanted to direct his staff and not let thenm talk to thos nasty matrix people; and once where a senior developer thought he could carry on building castles in the air instead of putting something concrete together because he wasn't being pressured enough, while senior line managers were fighting to have a traditional system with no dotted lines, only - at most - occassional short term secondments of their staff to other projects with the secondment terminable at their absolute discretion. Both times it ended up in disaster. I've seen dotted lines work extremely well dozens of times.