Whatever joining procedure used, somewhere there is the possibility of aircraft to aircraft conflict.
Aircraft already in the pattern, whatever climb angle they might make, have priority over joining traffic.
"See and be seen" is subject to the limitations of the human eyesight.
There was a discussion here (Private Flying) very recently where a newly qualified pilot told us about a situation where he used the radio to ask another pilot for his position. He was concerned that someone took him to task on the radio for doing so, as did others participating in the discussion he began here.
Some others here will hopefully see that what he did was actually very sensible, irrespective of what some folk think CAP413 doesn't allow us to say on the radio. Safety is paramount. If in doubt, use the radio in any way you need to.