Information below is gathered from discussion with a zabbix user.

When we delete an item from template, linked to 10K hosts, it takes too much time, and in 99% of attempts it returms nothing (supposedly PHP error happens).

There were changes in ZBX-6118, where it's stated:

Improved performance of create(), update() and template linkage methods for item, discoveryrule and itemprototype classes.

which does not include items deletion.

Besides of the zbx, there are also ZBX-13335, ZBX-13348, ZBX-13349 fixed, but they also do not talk about deletion.

And one more thing:
We have a user with limited rights, access to only one host group with ~500 hosts. When opening Configuration -> Hosts, page is loading very long time.
A super admin user opens the same page really fast.

Zabbix 3.4.9. © 2001–2018, Zabbix SIA                           
******************** Профилировщик сценария ********************
Всего затрачено времени: 1593.176998                            
Всего затрачено времени на SQL: 0.072697                        
SQL запросов: 46 (selects: 44 | executes: 2)                    
Пиковое использование памяти: 14.25M                            
Лимит памяти: 512M                                              

Note - I'm not sure what the provided debug belongs too - opening a page or deletion items.
Strange thing that debug section does not contain some fields if compare with a testing zabbix installation.