Of the aircraft you mention, the PA-38 is the only one designed as a trainer. Unfortunately, trainers tend to be 2 seaters so they are not good income earners for a school when it comes to renting aircraft so schools tend to opt for the PA28 as a general purpose aircraft. The PA28-140 is a better trainer than the PA28-161 for the very reason you state. They also need to consider how tough an aircraft is, the C152 and PA28 have survived the course of time wheras many of the more modern and plastic aeroplanes need very careful use and will not survive years of training.
Are glass cockpits better than gauges?
Glass cockpits are guages, but there are invariably too many for training, diverting the student from what they should be doing, looking out of the window, and can all fail together unlike conventional instruments.
You would probably find the best trainer is an old fashioned tail dragger with just the basic instruments, you would be a more skilled pilot than someone who has learned in a Technam.