It's great that you point out the limit on number of columns of many databases (typically 255, but check your specific database!)
I don't think SQL people will necessary beat anyone up for having lots of columns. After all, for a customer record, we don't create separate property tables for "name" and "email address" and "mailing address line 1." If you think this table is fine:
CREATE TABLE customer(
customer_id NOT NULL INTEGER,
name VARCHAR(255),
email VARCHAR(255),
address1 VARCHAR(255),
address2 VARCHAR(255),
mailing_code VARCHAR(255),
mailing_city VARCHAR(255),
mailing_country VARCHAR(255),
phone VARCHAR(255),
PRIMARY KEY(customer_id));
Then why is this table bad?
CREATE TABLE character(
player_id NOT NULL INTEGER,
character_id NOT NULL INTEGER,
strength INTEGER,
dexterity INTEGER,
mana INTEGER,
swords INTEGER,
polearms INTEGER,
shields INTEGER,
dodge INTEGER,
swimming INTEGER,
PRIMARY KEY(player_id, character_id));
If you specifically use MySQL/InnoDB, you can even make your tables allow adding more columns without having to update table stores, by pre-creating 255 columns as nullable, named "future_01," "future_02" and so on. Nullable columns end up only taking a bit in the record when they don't have a value, and you wouldn't be referencing them. Then, when you introduce a new skill, ALTER TABLE RENAME some future_ column to the skill you need. That's a very fast data dictionary update!
I also don't understand why serializing out of a single row would be any more or less work than serializing out of a self-join table or out of a BLOB/TEXT field. You still have to look up the string "strength" to some integer variable somewhere, and you very likely want to write that as some kind of IDL that generates code from schema, rather than manually doing it, no matter which of the options you choose.
For most smaller games, the one-row-per-character option is actually surprisingly usable, and surprisingly easy to work with. You only need to bring out the bigger guns if your design and implementation actually exceed what you can do with that initial approach.