I thought I'd replied by pm yesterday but my pm seems to have vanished. (First time I'd tried to send a pm here so maybe I'm not yet familiar with the workings.) Anyway, since others are interested I'll just post my response.
I'm a US citizen and bought and own my apartment solely in my own name. There was no legal obstacle.
To transfer ownership of an apartment, I suggest you enlist the services of a 代書 (daishu), not an accountant, because this is what daishu specialize in in Taiwan. An accountant would only be useful if you have related tax questions. But a daishu should also be able to answer your real estate related tax questions, so there's no reason to get an accountant involved except in an unusual case. (See details of the daishu I used at the bottom of this email.)
I don't know why people often say that foreigners can't buy residential property in Taiwan. There is absolutely no truth to this. The only restriction on the purchase of ordinary residential property is the condition of reciprocity. That is, to be eligible, the foreigner must come from a place that allows Taiwan nationals to purchase property. However, must advanced countries in the world meet this criterion. When I bought my place, no one specifically asked me what state I'm "from." My US passport at the time gave my place of birth as Illinois and the place of issue of the passport as Hawaii. If the issue comes up in your case, then sure, why not use California to be safe (if you have a connection to the place), since lots of Taiwanese obviously own property in CA.
I think in the case of married foreigners, the local spouse often may feel that it is simply easier (or in some cases more secure for them -- though not suggesting by any means that this true in the OP's or anyone else's particular case) just to own the house in their own name, rather than own it in two names. However, this really is just a matter of a bit of extra paperwork. Another consideration may be that Taiwan nationals meeting certain criteria (depending on the gov't policy in place at the time this may include age, purchase of first home, etc.) may be eligible for certain tax incentives or mortgage incentives from the government. Note that while foreigners may not be eligible for some special government incentives for first-time home purchases, they ARE eligible for the standard property tax incentive given by the government on one's primary self-owned home of residence. (I know this because I registered for and enjoy this tax benefit myself.)
A separate issue for foreigners married to a local is that locals may qualify for a more favorable mortgage rate from the bank. But that shouldn't bear on the issue of whether the foreigner gets their name on the deed, because as long as the local spouse is signing, co-signing, or guaranteeing the mortgage, the banks shouldn't mind too much whether a second name is on the deed of the house, especially if both spouses are signing the mortgage. (In my own case, I was able to negotiate a mortgage without a local co-signor.)
In short, even if I had been married at the time I purchased the apartment, I still would have insisted on having my name on the deed. Even if it meant paying a slightly higher mortgage or missing out on some small government incentive, I'd be willing to pay the extra amount for the satisfaction of having ownership in my name, or shared in our names.
The 代書 office I used for the ownership transfer is the one below. (This is their banqiao branch, which is the one I used. They have other branches too.) Not sure how much, if any, English they speak though.
http://www.kingmen.com.tw板橋所:新北市板橋區館前東路116號4樓之2 TEL:(02)2953-3366
Good luck!