The problem with these sorts of threads is that people describe what they do (washing sequence, type of washer, etc) but do not explain the efficacy of their particular washing procedure.
Discussions about the usefulness or effectiveness of any particular methodology is pointless without evidence of appropriate testing to identify if such methodology delivers archival standards (should that be your aim of course).
Many people use the Kodak HT-2 spot test. However, this can give misleading results because you are only testing one spot and are assuming that the whole print has received the same level of washing as they test spot (for a comprehensive understanding of the washing process, I would recommend reading Mysteries Of The Vortex which is a thorough investigation of the subject conducted by Martin Reed and which is available on the UK analogue photographers site:
http://www.film-and-darkroom-user.org.uk/forum/showthread.php?t=296&highlight=vortex).
The most effective test for determining a thorough washing methodology, is to immerse a complete print that you believe that you have thoroughly washed in the HT-2 solution. When I periodically test with this solution (typically when I have moved darkroom - thus encountering the possibility of different quality of water - or the washaid that I was using has been discontinued) I use the ANSI PH4.8-1978 formula published by Ansel Adams in the 1980 version of The Print:
Distilled water 750ml
Glacial acetic acid 30ml
Silver Nitrate* 10g
Distilled water to make 1L
Mix in the sequence above.
*Note great care needs to be taken with Silver Nitrate as it is a poison! - you should wear suitable protective clothing and only use in a very well ventilated space.
If the print (both front and back) show any staining, however faint, then your washing sequence is not delivering prints that have been washed to archival standards.
So back to the OPs original question:
If the Ilford wash sequence works for you (subject to adequate testing of course) then you will have no benefit using a dedicated washer. If the sequence works for you but you plan to do more prints per session, then you may find that the Ilford sequence becomes much more time consuming because each print needs to be washed separately. In this case you may find a dedicated washer more advantageous.
Perhaps the greatest benefit of using an efficient* archival print washer is that you can leave the prints to wash at the end of a printing session and get on with something else. In my case, I may get on with mounting prints from a previous printing session or go home for my supper or go to the pub for a couple of beers.
*If you read Martins treatise on effective washing of prints, he clearly demonstrates that being able to dump the majority of water in the archival washer at the 10 - 15 minutes stage of a 60 minute wash makes an enormous contribution to the efficacy of the washer. Previously this was only available with the Salt Hill washer and Martins own design that Silverpoint sold (now sadly discontinued). Of those archival washers currently available, I believe Nova now offer a washer with this total dump facility.
Bests,
David.
www.dsallen.de