Most DSLR cameras use external memory chip to save images. Why don't they use large internal memory?
There is nothing technical stopping DSLRs from having internal storage (in fact, they already have a small amount).
One reason for not including internal storage would be that it cannot be replaced, both in the short term (once the memory is full) and in the long term (once the memory, which would most probably be flash memory, starts to fail).
Having the replaceable memory (i.e. SD cards, CF cards etc.) allows the photographer to swap out each card as it finishes, meaning more photos before having to sit at a computer and spend time, which could be used taking photos, getting the photos out off the internal memory of a camera.
Replaceable memory also means that memory failure (which is likely at some point) doesn't ruin a camera instead only a small cost is incurred, rather than the cost to replace or repair the camera.
Also professional photographers may use their cards as an extra form of permanent backup, storing the cards from each project and never reusing them.
Including built in memory is also more cost, making the camera more expensive to manufacture.
damned truths covered most of the points, but I'd also like to mention the word "large".
The way things have been going over the past few years, something that looks large today could end up looking tiny in only a few years.
With cards, it's easy to get something larger, and if it's something that's readily available (SD, CF), you effectively have infinite storage capacity - and the possibility of using an external reader so earlier cards can be read while the shoot is still happening.
Also, there is an aspect of data confidentiality here.
Once you remove the memory card, the only thing you have to handle as bearing potentially confidential data is that card. This will allow for clean separation of data and camera. Eg you do work for client A, put the card under lock and key, and can take the camera to client B without having to worry any data of client A being accidentally displayed, falling into the hands of a camera thief. The same applies if you want to loan or sell the camera away, or return a borrowed or rented camera.
Technically, there are exceptions - a really dedicated attacker (in the infosec sense) could probably get some (few) images from the buffer(s) even if the camera does no longer offer access to them.
In the comments to the accepted answer there is a comment about why not have both internal and external?
I have that on my JVC video camera.
I like that if I forget my card at home then I can still record.
Countless times have I "lost" video files only to realize months later that they are saved on the internal memory card.
The camera switches from SD to internal automatic when SD is full, which is great, but I don't usually connect the camera with cable.
It's good but also it's a pain to have to look at both memories just to see if something was saved there.