Q: Is there some way I can ask Apple to provide a web based app to access my keychain passwords like Lastpass so that if I find myself in a situation where I lose my iPhone and dont have my Mac with me I can still get access to my passwords?

http://www.apple.com/legal/intellectual-property/policies/ideas.html

You can provide feedback and make suggestions via Apple Feedback: http://www.apple.com/feedback/icloud.html

You can suggest it, but i highly doubt they would ever do that.  Putting people's keychains on a web site inherently increases the insecurity of the passwords and I don't think Apple would accept that risk.

As it is now, your passwords live only on your Apple devices, and in your iCloud account.  The are encrypted with strong AES encryption during both transmission between your Apple devices and iCloud, and as stored on iCloud, and they are inaccessible on iCloud itself - they are only human readable to you on your devices with your security credentials.

Passwords stored and accessible on any web site are inherently less secure.  As always, security and convenience are mutually exclusive concepts.

The way that LastPass (and Dashlane) make the data available by logging in to a website is that it is first downloaded to your device and then decrypted locally.

Then I guess I don't understand the OPs idea.  If you don't have your computing or mobile devices with you, then what does an online or offline web access password manager offer?  I assumed they wanted to be able to use any old browser available and get their passwords.  If you have your devices available. you can just connect to your iCloud account and use iCloud keychain?

I certainly would never use any computer that was not mine to download and decrypt my passwords to the devices common storage (and you'd need permission to install the browser add-in to access those sites)?

Anything that requires download and local decryption is only ever safe if used on your own trusted devices.

In my case it was to my wife's Windows computer. I could have installed Dashlane on it but I rarely use that computer and it was slightly easier to do it via the web access. I don't use iCloud Keychain because I need something for both Apple and non-Apple devices.

I'm not suggesting or thinking Apple is likely to do it -- only trying to answer the OP's question of "Is there some way I can ask Apple ..."