Yes, but you have to be on that company's radar, before they add it to the list. (Something unlikely to happen en masse before your startup is large enough to handle it appropriately.) And in the case of copyright takedowns, the extreme volume comes in part from the fact that Google and other companies of that size have even implemented bulk reporting tools explicitly designed to permit requests of that type and volume that the average user, or even corporation, doesn't have access to.

I don't know the answers to these, but I'd wonder if RTBF would allow for you to set restrictions on who can submit requests on behalf of who, or the volume permitted by a given reporting entity, or the level of automation permitted in reporting. Presumably the EU would much rather than you make reasoned, well-thought responses to carefully considered and submitted removal requests, over a bulk import/bulk decision process that leads to a lot of incorrect behavior.

Do you have a concrete reason why you think it's unlikely? I have a different opinion about how large a search engine company would have to be before being able to "handle it appropriately", but maybe you have a good argument that trumps my experiences.

I don't think I could offer anything solid, no, beyond the general view that the litigious folks generally don't approach a platform before it's significantly large. (Most piracy on smaller mediums goes unharassed, for example, while The Pirate Bay and YouTube gets most of the attention.)

A friend of mine runs a video copyright enforcement company. He provides the ammunition that Hollywood uses to send takedowns to a large number of small video platforms for content posted on them.

For a web-wide search engine, it's even easier: you can send a search engine a takedown for any url anywhere, because search engines index the whole web. RTBF requests are similarly relevant to any web-wide search engine.