Ok, knowing a little about you and your diving, that you are or aim to be DIR and use a BT - i feel the question is loaded of sorts, but i will bite. I am still waiting on my computer at this time due to mailing problems, so here are the why's and my ideas on how i am going to try to plan my dives.
1. Most other people use them, we also use computers nowadays instead of typewriters, and cars instead of walking (although i have a health problem with that idea). They should run off the same kind of model as the tables that OW divers are trained in, although the actual algorithm might have certain penalties or liberalisms for your actual dive profile compared to the rigid table value, regardless of your diving attitude/style. I think it is technological advantage over the table format that tailors the actual dive to you, not a generalisation.
2. The algorithm works off your actual profile compared to a rough square profile, which can add considerably to your actual time underwater. It can give you other dive specific details, but you can also get those off a BT on your wrist (depth, max depth, ascent rate, time, temp). The advantage is that you have essentially a "table" like value in front of your to check anytime, just like you might put on your slate with your dive plan (so far with tables that is what i do and note the actual info if it was shorter than the dive plan).
3. I will use the table value, or max bottom time of the computer for the planned depth (computer (Suunto) time is less than PADI RDP) to get a feel for when i would plan to leave the bottom (if no other factors will affect, like air for instance). After the 1st dive i will assume a reduction on the table value after the SI to give me an idea of how long i can go down the 2nd+ dive, so i have an idea of bottom time again, not just relying on what is being spat out by the computer at depth. I would read across the table with my approximate dive profile (in a multi-level style) then put in my SI to find the reduction amount on the tables and check that against the computer's estimate. I understand the values from reading across the table give similar results to the wheel, with rounding, but could still be approximated. I plan my max time at depth prior to diving, i will just use the computer to keep track of my "actual" nitrogen loading and analyse this value throughout and after the dive against my plan. I will use this for actual bottom time at depth, then work my way up using the computer (initial bottom time from "tables"), but not riding the NDL's as i rise up, but in a methodical way or stops and fairly slow ascents between stops.
4. Havent got computer yet, so it would be new. Assuming a battery problem, hopefully the battery life indicator will show me that trouble coming, and replace on SI or before a longer trip. If its due to flooding, surprisingly enough i guess i wouldnt be able to use the computer for the rest of that day (assuming i could find somewhere to get it fixed). I do note various things on a slate and have a back-up watch for timing. I was thinking of getting a BT as a back-up as well, but funds are being spent oh so quickly at this time! In the future hopefully. As far as i am aware you can recall the last 9 dives on a BT, so that would be more than enough to table off a day of diving and continue (assuming i am not off the tables completely, more than likely) possibly making some assumptions and maybe taking an extra long SI and assuming an extra high ending PG before the SI. Worst case i just quit diving the day and start again the next on tables, or buy a back up more liberal computer.
5. The OW training didnt cover them too much, but we went through some stuff on multi-level and computer use in AOW as well as many other things.
I know you dont need one, and you can dive tables, i know its not officially taught that you can use tables by reading across them, and that you should buy another piece of plastic for $30-40 to do mutli-level, but it seems to match up pretty well. Its a personal decision. Wendy, what do you use to plan, just tables, or the desktop computer based planning software (i dont know if you do deco diving or not, i know you are cave or very nearly)??? When i move towards diving that requires deco, i will probably use these computer programs and use my dive computer in guage (which makes it a very pretty, but expensive BT). Will continue to discuss that with my instructor though as the time comes. I know that he runs the deco software and dives off of that info, whatever his multi-gas ($1000+) computers are telling him. But what is the real difference in planning off that software or actual tables or watching the computer, they all churn out numbers, its just that the computer churns them out based upon your actual dive profile, which hopefully is very similar to your plan.
