Which bitcoin wallet allows me to generate and export a large number of addresses? I need a software Bitcoin wallet (not web account based) that allows easy generation of many new payment addresses at once that are ideally stored in plain text, (bulk exported as plain text). The security is not a concern. 
I like Bitcoin-Qt but it is outdated and it takes forever to download the entire chain, which make it not portable in a way.

Is it necessary to download the chain? If one can use a paper wallet than one must be able to use software one without having the blockchain, or having just a small number of blocks, right?
It is not necessary to download blockchain to generate address. Use an HD wallet like electrum, so that you can regenerate wallet using seed even if you lose private keys.

To generate addresses http://docs.electrum.org/en/latest/faq.html#how-can-i-pre-generate-new-addresses
To export addresses use electrum command line http://docs.electrum.org/en/latest/cmdline.html