you can not just put a sump pit in without fix the problem,

it will comeback.

snake a camera in is a good idea, cost $300 to $500, if it determent it is the outside pipe, replacement is about $800.

if perimeter tiles are clog, these are tiles outside of the house, buried along the wall, they can replace for about 2k.

now if you determent the underslab tiles are clog, then you need to cut the concrete, put in new weep lines and also a sump bit.

the reason I am asking if you know where the water coming in is,

if the water come from one corner, and that is where the drain line goes to the street, mostlikely that drain line is clog.

if the water come from 4 walls, perimeter tiles maybe the problem.

if the water shooting thru the saw line on concrete, then the underslab tiles are the problem.

you are right, there is no need to replace the whole system. them contractors are BSing you.