I can't.... is someone seriously arguing that having a mini-map on screen would be distracting? Is this real life? Is Splatoon the first shooter you've played?
I've already described squid beacons to you, put them in a small list or simply let the player to cycle through them using the D-Pad.
That's the thing, how would the list refer to the Squid Beakons? Numbering them won't work because you'd run into the problem of having to look up a number in order to find the beakon you want to jump to, instead of just immediately selecting the beakon itself. And I hope you realize how slow cycling through the beakons (+ other jump points) would be in comparison to how the touchscreen works.
Also, a lot of shooters don't keep entire maps visible on screen during normal gameplay, usually a radar system or something of the sort. Furthermore, maps that do get displayed are typically as barebones as possible to prevent screen clutter. Let's contrast that with Splatoon which can have:
-Ink trails (which can potentially mask enemy/ink colors behind it)
-Teammate locations
-Enemy locations
-Object locations (Squid Beakons, Mines, etc)
-Objective locations and statuses
All of these need to constantly be on display in order for the map to work as it does now. Are you going to argue that the combination of all of these elements would not be distracting or take up a lot of screen real estate?
There can only be 4 on the map at a given time from your team.
Wrong. There can be up to 12 Squid Beakons, 3 per teammate. The spawn point and the 3 teammates brings the maximum possible amount of jump points to 16. Good luck trying to sort through that in quick fashion.