Under what conditions?
If the contacts are already closed and seated, a pretty fair surge current could be handled. There may be momentary contact melting, and the contacts will settle into a more stable position which could handle even more, perhaps.
This, plus the mention of surface contamination, oxides, whatever, is where "wiping current" comes from. The contact points can be incredibly microscopic indeed: the surfaces might be within nanometers, or fractions thereof, so that current flows through tunneling as much as bulk current flow. The points may be nanometers or micrometers wide; wider of course when made to melt some, or to slide past each other to push dust aside and abrade down some peaks.
Given higher currents and some clamping and sliding forces, multiple contact points can be made, which may be relatively wide (10s or 100s of micrometers?), and high currents can be handled without (further) local melting.
Heh, or you draw juuust too much and vaporize the point contacts and end up blasting them apart and an arc forms, melting the surface, then either a still-stronger contact results (which the spring may not be able to open anymore

), or it repeats ad nauseum...
If the contacts are open, and closing to a very low impedance (voltage source, capacitor discharge), yeah no. Start directly in the arcing phase. (At above 30V or so, air breaks down in microscopic gaps -- no contact required. At lower voltages, the contacts may touch physically, and any sparking is initiated by blowing out the initial contact points.) Maybe they'll touch and weld together, maybe they'll just blow apart and crater. Remember it takes whole milliseconds for the contacts to move; if the spark is over in some microseconds, it'll be all arc and cratering, and no wiping.
For something like spot welding, there are many ways to work with it:
1. Use a transformer, possibly with mains power, but it can be pulsed (from a capacitor) as well. The higher voltage is somewhat harder to make and break (the arc starts from a longer distance), but the current is lower and that's the big deal. It's a lot easier to switch 10s of A than hundreds or thousands, even if the voltage is higher.
2. Use MOSFETs. Kind of a pain since you're going to need a bunch in parallel, and need to make sure they behave together, and don't destroy themselves; but it works, and indeed, exists:
https://www.keenlab.de/index.php/product/kweld-electronics/3. Use SCRs. These latch on, and are capable of sinking thousands of amperes even in modest packages (TO-218 sized, say). They do have a modest voltage drop (1-2V) when on, they can't be turned off, or not easily at least (fine for a capacitor discharge application), and do need some precautions to avoid destroying them (dI/dt may need to be limited by series inductance). (They eventually turn off when current drops, then can ready for another cycle.)
Tim