YES. One hundred times yes.
Merseyrail is only good for people living in the north of Liverpool or along the river. (I won't speak for the Wirral since I don't live there.) Anywhere else, it's useless. The suburbs are incredibly disconnected not only from Town, but from themselves. Its intercity service is good for Southport northward (north bias again) but for some reason Wigan eastward and Warrington southward (kind of) are excluded despite being similar distances.
Electrifying the Lime Street to Bank Quay (lower) route via Fiddler's Ferry is perhaps the most obvious addition to Merseyrail and it's shocking people talk about it like it's pie-in-the-sky stuff. The line via Speke and Sefton Park are sorely missing services, and the tracks and half of the OLE are already in place!! The Loop Line via Gateacre is the second most obvious, since a "main line" loop connecting most of the city and bringing services to the currently car-dependant suburbs is a HUGE deal. Statistics of rail usage per borough (?) show this without a shadow of a doubt.
Source: LCR's 2023 Long Term Rail Strategy.
It makes a lot of sense, but it does require some more significant rebuilding, so I'd put it down as priority no. 5 on the top ten list of Merseyrail extensions.
My top 4 above that are (in descending order) -
1) Ellesmere Port to Helsby - easy to extend, improves connectivity between Cheshire and the Wirral/Liverpool, and it effectively restores service to Ince and Elton, a station serving several thousand residents already with the potential for a lot more housing and commercial development nearby.
2) Kirkby to Wigan/Skem - reinstates a direct train into Liverpool for a lot of people, after a gap of decades, as well as better and more reliable service from Wigan's suburbs into Wigan, and a potential park and ride upgrade of Upholland could take a lot of traffic off the M58 (congestion is generally not a problem on the road itself currently, but it is at the western terminus, Switch Island, where the M58, M57, A59, A5036 and A5758 intersect - a further rebuild to accommodate even higher traffic levels at Switch Island would be even more expensive but will have to be done at some point without alternative travel options to reduce traffic volumes.)
3) Bidston to Wrexham - a massive opportunity to connect a lot of the towns and villages of west Wirral to the rest of the peninsula and Liverpool, plus much better transport links for the somewhat deprived areas of Wrexham and Flintshire. Lower priority because funding will likely have to be secured from the Welsh government and it's a long extension which will need to be on battery, OR you'll have to fit some of the 777s with the OHLE equipment in place of a battery and find funding to wire an isolated island from Bidston to Wrexham.
4.) Ormskirk to Burscough Bridge (and potentially later Preston). Probably a joint scheme between Lancs CC and LCR. 1 new bay needed at Burscough Bridge for this plan, but improves connectivity between a large swathe of Lancs/eastern Liverpool and Southport, plus makes commuting or leisure trips from the growing town of Burscough into Liverpool much easier.
Rebuild both the northern and southern Burscough Curves for this plan - the southern curve is for Merseyrail and ends in the new bay provided on the south side of the station. The northern curve will enable direct Preston to Southport service operated by Northern, stopping at Burscough Bridge as an interchange for Ormskirk and Liverpool, but also restoring the well-used direct link between Preston and Southport on the railway (currently only catered for by the 2/X2 bus service, which is usually very busy, but susceptible to the heavy traffic on the A59/A565).