If there were nobody entering on the 45, as it is in Canada where rules require entry to the downwind from the midfield crossover, then I'd agree. Otherwise, I firmly believe based on decades of bad experiences that it does compromise safety. You have airplanes converging on one spot from three directions, and two of them will be belly-up to the other two. That means there's less chance of seeing each other, and one plane is trapped in the middle with nowhere to go if a conflict develops. As far as I'm concerned, the area inside the pattern is a no-man's land where I don't want to be, and I don't think anyone should plan to be.
What of operations that drop jumpers into the middle of the field. Should no one be over the field?
When one enters the downwind on a 45, as often as not the actual intersection with the downwind leg doesn't actually occur at midfield. It may occur closer to the departure end, or closer to the approach end of the runway. It all depends what other traffic is in the pattern. There may already be traffic on crosswind, on downwind, and on base. To fit into that pattern one may join abeam the numbers, rather than farther back, or one may fall in behind the downwind traffic.
This is no different than arriving on a crosswind that passes midfield, or over the numbers, or over the departure end. It's still an entry to the downwind at whatever point it intersects the downwind, and directly over the field is often the safest place to be.
With that in mind, it doesn't matter much if one is entering the downwind from the right or left. The goal is to set up to land and to do it without dinging the airplane or another.
I flew into the Grand Canyon airport for several years, flying tours, ferrying river runners, doing fire patrols, and so forth. GCN used to have multiple patterns for the single runway in use. Right and left down winds would be in use, as well as inner and outer down winds, and high and low down winds. That's a left inner and outer, upper and lower: four down winds on one side, and four on the other, to the same runway, as well as helicopter patterns (multiple patterns) arriving and departing at the same time. No radar. The pattern was often full, with a steady stream of departures, as well. It was one of the busiest single runways in the world.
Fast traffic flew outer patterns, slower traffic flew inner patterns. One might be told to stay high, extend downwind, join farther upwind, or so a number of things, as necessary, to manage traffic. It wasn't uncommon in a pinch to be told to do a 360 for spacing.
The notion of the example traffic pattern as prescribed in the AIM and various other sources is just that: an example, not a cookie cutter rigid form.
Various entries into the pattern doesn't change the nature of the pattern: there's still a downwind, base, and final, and this is true whether one joins the downwind on a 45 or enters it from an overhead midfield crosswind, or from over the numbers. It's the same. The pattern is not demolished, diminished, or destroyed.
I may fly a traffic pattern very close to the runway in one airplane, but much farther away from it in another. The type of aircraft I'm flying and the speed make a difference. Not every pattern is flown the same distance from the runway, and per the AIM, not every pattern is flown at the same altitude. What of the turbine single engine airplane that's slower than other piston aircraft in the pattern, but that's supposed to fly a 1,500' altitude, where the piston airplanes are below, in the same pattern, at 1000'? Is this a wise idea? I think not.
Not too long ago we did some training in a Cessna 180. Our patterns were tight to the runway, perhaps inside what others might do. We hopped from airport to airport, some of which had students dropping in from large flight schools. I noted that many of the students flew big, wide patterns, as one sometimes expects of the students. I might already be in the pattern, and find that the students began flying so wide from the runway on the downwind that I'd lose track of them. Seeing as they were flying the same general rectangular pattern prescribed by the AIM, some here might be inclined to say that they're not harming the essence of flying the traffic pattern, although certainly their actions were distracting and they were hard to see. I might be on a downwind leg, the same leg I'd been flying for the last hour as I went around the pattern, and find the new arrival is on a base leg ahead me and well to my right...because they flew the pattern so wide that they're crossing my path on the base leg. Hardly a good idea, but perfectly acceptable under the rigid square pattern theory. None the less, we have those here who would decry anything else.
I've had traffic on a straight in advise me to land first, while I'm on the downwind. From in close, directly abeam the numbers, I could easily make the numbers, and have, without any disturbing of the arrival of other aircraft. Simple agreement and discussion, and it's done. Conversely, while dropping jumpers, I've entered the downwind at 18,000' in a Caravan and made the numbers without any problem, after putting jumpers out over the field. I've done it with full concurrence with ATC and a clearance, no concerns at all. It made as much sense as going somewhere else to descend, then returning to the field to enter on a 45. In fact, it made more sense.
A week ago while working an active fire only a few miles from an uncontrolled field, we made our returns directly to the airport, over the runway, and onto the downwind at our cruise speed, and retarded the power abeam the numbers for a tight turn to final. Our departure was an immediate turn to the fire. We made good progress with the fire. No structures or homes were lost. We received a thank you from a dozer operator who took several loads over the top of his equipment, when he got in trouble. The fast turns and immediate access to a loading point made all the difference. I'm sure someone might say it's just not proper to have not flown well away from the airport on the downwind side, then made a perfect 45 entry to the downwind, but that wasn't happening, and didn't.
Once during that time I arrived at the runway with a helicopter, and approximately the same time. It was an Army National Guard helicopter with whom we were working. I coordinated staying low with a tight turn to land, and the helicopter followed me in. They only needed fuel; I needed to load and go. I passed them on the downwind, with their concurrence, landed, and they landed behind me on the taxiway. Problem solved. It's just not a big deal. A little courtesy, a little communication, seeing and avoiding, and moving on.
Those who whine about a midfield crosswind or other entries to the traffic pattern (let's call them arrivals, for that's what they are) that blend seamlessly with the flow or potential flow of traffic are the same people who cry that the sky is falling if the world doesn't match their ideal of a cookie-cutter image. For those of us that fly where the rubber meets the road, a little more flexibility goes a long way. So long as it can be done safely, and it can, then we'll keep on doing it that way.
That includes making straight-in approaches to land.